M. Kida, “Reduction of Elliptic Curves over Certain Real Quadratic Number Fields,” Mathematics Computation, Vol. 68, 1999, pp. 1679-1685. doi:10.1090/S0025-5718-99-01129-1
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.