On the conductor of an elliptic curve with a rational point of order 2

Let C be an elliptic curve (an abelian variety of dimension one) defined over the field Q of rational numbers. A minimal Weierstrass model for C at all primes p in the sense of Néron [3] is given by a plane cubic equation of the formwhere aj belongs to the ring Z of integers of Q, the zero of C being the point of infinity.