American Journal of Computational Mathematics
Volume 2, Issue 4 (December 2012)
ISSN Print: 2161-1203 ISSN Online: 2161-1211
Google-based Impact Factor: 0.42 Citations
On Elliptic Curves with Everywhere Good Reduction over Certain Number Fields ()
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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.
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