June 21, 2024Open Access

Torsion of Rational Elliptic Curves over the Cyclotomic Extensions of Q

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Abstract

Let E be an elliptic curve defined over Q. Let p>3 be a prime such that p-1 is not divisible by 3, 4, 5, 7, 11. In this article we classify the groups that can arise as E (Q (ₚ) ) ₓ₎ₑₒ up to isomorphism. The method illustrates techniques for eliminating possible structures that can appear as a subgroup of E (Q^ab) ₓ₎ₑₒ.

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Ömer Avcı (Fri,) studied this question.

synapsesocial.com/papers/68e63e20b6db6435875cfbcd https://doi.org/https://doi.org/10.48550/arxiv.2406.15606

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