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Elliptic Curves. (MN-40)

Elliptic Curves. (MN-40)

Penned By Anthony W. Knapp
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4.85
27,793 Global Ratings
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Elliptic Curves. (MN-40)

Elliptic Curves. (MN-40)

Penned By Anthony W. Knapp
4.85 27,793 Ratings
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Editor's Note:
An elliptic curve is a particular kind of cubic equation in two variables whose projective solutions form a group. Modular forms are analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem. Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L functions match. The theory covered by Anthony Knapp in this book is, therefore, a window into a broad expanse of mathematics--including class field theory, arithmetic algebraic geometry, and group representations--in which the concidence of L functions relates analysis and algebra in the most fundamental ways. Developing, with many examples, the elementary theory of elliptic curves, the book goes on to the subject of modular forms and the first connections with elliptic curves. The last two chapters concern Eichler-Shimura theory, which establishes a much deeper relationship between the two subjects. No other book in print treats the basic theory of elliptic curves with only undergraduate mathematics, and no other explains Eichler-Shimura theory in such an accessible manner.

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Released October 5, 1992
Identifier (ISBN) 2132098
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Anthony W. Knapp
The Mind Behind the Work
Anthony W. Knapp

After spending years working in the corporate world, Anthony W. Knapp finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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George Baker
George Baker September 27, 2025
"Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre."
Sharon Anderson
Sharon Anderson December 12, 2024
"Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
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Stephanie Allen
Stephanie Allen December 13, 2024
"I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
David Collins
David Collins April 22, 2025
"A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre."
William White
William White April 30, 2025
"Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars."
Dorothy Harris
Dorothy Harris February 27, 2025
"A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me."
Barbara Rivera
Barbara Rivera April 07, 2024
"A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel."
Kimberly Adams
Kimberly Adams May 12, 2025
"Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
Edward Flores
Edward Flores October 04, 2024
"Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece."
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"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
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Patricia Evans November 11, 2024
"Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading."
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"I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty."
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"Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
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"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
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"Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall."
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"Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
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"Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
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"Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel."
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"Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece."
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"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
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"Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
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"Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall."
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"Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Linda Wilson
Linda Wilson September 13, 2025
"I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author."
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"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
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"I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece."
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"I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
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"Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers."
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"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre."
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"Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author."
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"Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel."
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"I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author."
Ryan Lewis
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"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre."
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Sandra Gonzalez
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"Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
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"I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall."
Mark Allen
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"Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
Amanda Baker
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"I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me."
Richard Evans
Richard Evans May 29, 2024
"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
George White
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"Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers."
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Amanda Parker April 21, 2024
"Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading."
Anthony Wilson
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"A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall."
Amanda Baker
Amanda Baker October 07, 2024
"Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
John Moore
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Steven Miller
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"A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me."
Lisa Phillips
Lisa Phillips June 17, 2024
"Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me."
Mark Jones
Mark Jones July 22, 2025
"Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
Edward Diaz
Edward Diaz May 07, 2024
"I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall."
Donald Harris
Donald Harris August 20, 2024
"A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
Karen Brown
Karen Brown November 12, 2025
"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author."
Kimberly Young
Kimberly Young August 21, 2024
"Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
Ashley Thompson
Ashley Thompson February 25, 2025
"I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece."
George Wilson
George Wilson January 29, 2024
"Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers."
Amanda Jackson
Amanda Jackson February 11, 2025
"Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem."
Linda Phillips
Linda Phillips July 13, 2025
"Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers."
Amanda  Parker
Amanda Parker October 23, 2025
"An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. Suitable if your reading queue is empty."
Donald Martin
Donald Martin November 04, 2025
"Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars."
Deborah Jones
Deborah Jones March 24, 2024
"Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty."
James Gonzalez
James Gonzalez April 29, 2025
"I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece."
Andrew Brown
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"Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading."
Jessica Johnson
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"Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece."
Linda Harris
Linda Harris November 28, 2025
"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
Michael Allen
Michael Allen August 07, 2024
"Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece."
John Thompson
John Thompson October 07, 2024
"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
Karen Brown
Karen Brown October 21, 2025
"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author."
Amanda  Davis
Amanda Davis April 12, 2025
"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
Patricia Anderson
Patricia Anderson March 23, 2025
"A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. A fair 3 stars."
Patricia Hall
Patricia Hall May 24, 2025
"Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading."
James Adams
James Adams April 30, 2024
"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
John Moore
John Moore January 01, 2025
"A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall."
Paul King
Paul King October 04, 2025
"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre."
Karen Miller
Karen Miller February 09, 2024
"An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes."
Donald Clark
Donald Clark March 24, 2025
"Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers."
Joshua Miller
Joshua Miller December 16, 2024
"A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author."
Charles Martin
Charles Martin September 28, 2025
"A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes."
Edward Diaz
Edward Diaz March 27, 2025
"Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading."
Mark King
Mark King February 09, 2024
"I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
Karen Campbell
Karen Campbell December 15, 2024
"I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me."
Linda Evans
Linda Evans March 13, 2024
"A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend."
Betty Harris
Betty Harris December 11, 2024
"A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel."
Ryan Evans
Ryan Evans June 11, 2024
"Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author."
Donna Cruz
Donna Cruz December 18, 2025
"Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
Deborah Gomez
Deborah Gomez February 03, 2024
"A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
Stephanie Phillips
Stephanie Phillips March 12, 2025
"Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem."
Nicholas Cruz
Nicholas Cruz July 20, 2024
"A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers."
Karen Thomas
Karen Thomas April 25, 2024
"Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
David Williams
David Williams May 29, 2024
"Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem."
Ryan Thomas
Ryan Thomas July 29, 2024
"I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers."
Kevin Allen
Kevin Allen November 20, 2024
"Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece."
Rebecca Thompson
Rebecca Thompson August 25, 2025
"Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me."
Karen Adams
Karen Adams September 10, 2025
"Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece."
Patricia Clark
Patricia Clark March 27, 2024
"Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
Patricia Walker
Patricia Walker October 16, 2024
"An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time."
Michelle Gonzalez
Michelle Gonzalez September 17, 2025
"A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes."
Mark Martinez
Mark Martinez April 03, 2025
"Not entirely to my refined tastes. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time."
Steven Miller
Steven Miller April 20, 2025
"A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty."
Edward Ramirez
Edward Ramirez June 23, 2025
"I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece."
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