Rational points of order 7 | Zendy

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Rational points of order 7

Author(s) -

Dummigan Neil

Publication year - 2008

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdn093

Subject(s) - mathematics , rational number , isogeny , conjecture , order (exchange) , elliptic curve , rational point , pure mathematics , product (mathematics) , class (philosophy) , point (geometry) , combinatorics , algebra over a field , mathematical analysis , geometry , finance , artificial intelligence , computer science , economics , algebraic number

For an elliptic curve over the rationals, optimal in its isogeny class, with a rational point of order 7 but L E (1) ≠ 0, we prove that 7 divides the product of the Tamagawa factors with the order of the Shafarevich–Tate group. This is a small consequence of the Birch and Swinnerton‐Dyer conjecture.

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