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Families of elliptic curves with the same mod 8 representations
Published online by Cambridge University Press: 19 April 2017
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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