We describe an algorithm for determining elliptic curves defined over a given number field with a given set of primes of bad reduction. Examples are given over $\Q$ and over various quadratic fields.
@article{1204928531,
author = {Cremona, J. E. and Lingham, M. P.},
title = {Finding All Elliptic Curves with Good Reduction Outside a Given Set of Primes},
journal = {Experiment. Math.},
volume = {16},
number = {1},
year = {2007},
pages = { 303-312},
language = {en},
url = {http://dml.mathdoc.fr/item/1204928531}
}
Cremona, J. E.; Lingham, M. P. Finding All Elliptic Curves with Good Reduction Outside a Given Set of Primes. Experiment. Math., Tome 16 (2007) no. 1, pp. 303-312. http://gdmltest.u-ga.fr/item/1204928531/