Elliptic Curves Satisfying the Birch and Swinnerton–Dyer Conjecture mod 3
نویسندگان
چکیده
منابع مشابه
Rank of Elliptic Curves and the Birch Swinnerton-dyer Conjecture
We numerically verify the Conjecture of Birch and SwinnertonDyer concerning the analytic and geometric rank of an elliptic curve. An algorithm (based on the work of Cremona) is developed in the PARI/GP language for computing the order of vanishing of the L-function for any (non-singular) curve. The analytic rank outputs for several families of curves are compared with readily available data on ...
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We describe theorems and computational methods for verifying the Birch and Swinnerton-Dyer conjectural formula for specific elliptic curves over Q of analytic ranks 0 and 1. We apply our techniques to show that if E is a non-CM elliptic curve over Q of conductor ≤ 1000 and rank 0 or 1, then the Birch and Swinnerton-Dyer conjectural formula for the leading coefficient of the L-series is true for...
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Let E be an elliptic curve over Q, and ρl : Gal(Q/Q)→GL2(Zl) its l-adic Galois representation. Serre observed that for l ≥ 5 there is no proper closed subgroup of SL2(Zl) that maps surjectively onto SL2(Z/lZ), and concluded that if ρl is surjective mod l then it is surjective onto GL2(Zl). We show that this no longer holds for l = 3 by describing a modular curve X9 of genus 0 parametrizing elli...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1999
ISSN: 0022-314X
DOI: 10.1006/jnth.1998.2349