Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Elliptic curves with good reduction away from 2: II

R. G. E. Pincha1

a1 Emmanuel College, Cambridge

In this paper we continue the study of elliptic curves defined over a quadratic field S0305004100066196_inline1 with good reduction at primes not dividing 2 begun in [9] (referred to as I). We extend the results of I to show that such a curve must have a point of order 2 also defined over S0305004100066196_inline1 when d = −7, −3, −2, −1, 2, 3 or 5 and list all such curves over S0305004100066196_inline2.

(Received May 22 1985)

(Revised February 15 1986)