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- W4296454858 abstract "Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)otimes Q_p. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples." @default.
- W4296454858 created "2022-09-20" @default.
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- W4296454858 date "2016-10-27" @default.
- W4296454858 modified "2023-09-27" @default.
- W4296454858 title "Shadow lines in the arithmetic of elliptic curves" @default.
- W4296454858 doi "https://doi.org/10.48550/arxiv.1610.08729" @default.
- W4296454858 hasPublicationYear "2016" @default.
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