Construction Of High-Rank Elliptic Curves Over Q And Q(T) With Non-Trivial 2-Torsion

ANTS-II: Proceedings of the Second International Symposium on Algorithmic Number Theory（1996）

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摘要

We construct a non-constant elliptic curve, of rank at least 8, with a 2-torsion point, over the field Q (t(0), t(1), t(2), t(3), t(4)). By specializing the parameters to rational values, we obtain curves over Q with rational 2-torsion and of rank exactly 12, 13 and 14.

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关键词

High-Rank Elliptic Curves,Non-Trivial 2-Torsion

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