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- W2414264290 abstract "We establish a congruence formula between $p$-adic logarithms of Heegner points for two elliptic curves with the same mod $p$ Galois representation. As a first application, we use the congruence formula when $p=2$ to explicitly construct many quadratic twists of analytic rank zero (resp. one) for a wide class of elliptic curves $E$. We show that the number of twists of $E$ up to twisting discriminant $X$ of analytic rank zero (resp. one) is $gg X/log^{5/6}X$, improving the current best general bound towards Goldfeld's conjecture due to Ono--Skinner (resp. Perelli--Pomykala). We also prove the 2-part of the Birch and Swinnerton-Dyer conjecture for many rank zero and rank one twists of $E$, which was only recently established for specific CM elliptic curves $E$." @default.
- W2414264290 created "2016-06-24" @default.
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- W2414264290 date "2016-06-09" @default.
- W2414264290 modified "2023-09-26" @default.
- W2414264290 title "Congruences between Heegner points and quadratic twists of elliptic curves" @default.
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- W2414264290 doi "https://doi.org/10.48550/arxiv.1606.03172" @default.
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