On standardized models of isogenous elliptic curves

Samir Siksek
2004 Mathematics of Computation  
Let E, E be isogenous elliptic curves over Q given by standardized Weierstrass models. We show that (in the obvious notation) and, moreover, that there are integers t, w such that a 4 = a 4 − 5t and a 6 = a 6 − b 2 t − 7w, where b 2 = a 2 1 + 4a 2 .
doi:10.1090/s0025-5718-04-01690-4 fatcat:3sov3qawirhc5ob2jjuinime6y