Ranks of elliptic curves in cyclic sextic extensions of ℚ

2023/04/04 by Kisilevsky, Hershy, Kuwata, Masato
#11G05 #11G40 #14G05 #14G25 #14J28 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2304.01528

Abstract

For an elliptic curve E/ℚ we show that there are infinitely many cyclic sextic extensions K/ℚ such that the Mordell-Weil group E(K) has rank greater than the subgroup of E(K) generated by all the E(F) for the proper subfields F ⊂ K. For certain curves E/ℚ we show that the number of such fields K of conductor less than X is ≫√ X.

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