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Families of elliptic curves with the same mod 8 representations

Published online by Cambridge University Press:  19 April 2017

ZEXIANG CHEN
ZEXIANG CHEN*
Affiliation:
Nomura International Plc, One Angel Lane, London, EC4R 3AB e-mail: zexiang.chen@nomura.com
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Abstract

We compute certain twists of the classical modular curve X(8). Searching for rational points on these twists enables us to find non-trivial pairs non-isogenous elliptic curves over ℚ whose 8-torsion subgroups are isomorphic as Galois modules. We also show that there are infinitely many examples over ℚ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 165 , Issue 1 , July 2018 , pp. 137 - 162
Copyright
Copyright © Cambridge Philosophical Society 2017 

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