Abstract

We prove the existence and nonexistence of elliptic curves having good reduction everywhere over certain real quadratic fields Q(m) for m≤200. These results of computations give best-possible data including structures of Mordell-Weil groups over some real quadratic fields via two-descent. We also prove similar results for the case of certain cubic fields. Especially, we give the first example of elliptic curve having everywhere good reduction over a pure cubic field using our method.

Keywords

Elliptic Curves over Number Fields; Mordell-Weil Group; Two-Descent

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Conflicts of Interest

The authors declare no conflicts of interest.

References

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