W. Bosma, J. Cannon and C. Playoust, “The Magma Algebra System. I. The User Language,” Journal of Symbolic Computation, Vol. 24 No. 3-4, 1997, pp. 235-265.
has been cited by the following article:
TITLE: On Elliptic Curves with Everywhere Good Reduction over Certain Number Fields
AUTHORS: Shun’ichi Yokoyama
KEYWORDS: Elliptic Curves over Number Fields; Mordell-Weil Group; Two-Descent
JOURNAL NAME: American Journal of Computational Mathematics, Vol.2 No.4, December 31, 2012
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.