Fields of definition of elliptic curves with prescribed torsion

Peter Bruin; Filip Najman

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arXiv · 1607.05394

Fields of definition of elliptic curves with prescribed torsion

Peter Bruin·Filip Najman

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Abstract

We prove that all elliptic curves over quadratic fields with a subgroup isomorphic to $C_{16}$, as well as all elliptic curves over cubic fields with a subgroup isomorphic to $C_2\times C_{14}$, are base changes of elliptic curves defined over $\Q$. We obtain these results by studying geometric properties of modular curves and maps between modular curves, and then obtaining a modular description of these curves and maps.

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Peter Bruin, Filip Najman. 2016-07-19. Fields of definition of elliptic curves with prescribed torsion. https://arxiv.org/abs/1607.05394

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