Elliptic Curve Isogenies [closed]

Given a lattice L \in C with fixed basis {w_1, w_2}, Let \delta(L) = | w_1 \bar{w_2} – w_2 \bar{w_1}|. Let f : C/L ---> C/L’ be an isogeny determined by multiplication by a \in C{0}. Via composition, f induces an inclusion M(L’) ---> M(L). show that:

1. deg(f) = \delta(aL) / \delta(L’) = |a|^2 * \delta(L) / \delta(L’)

and

1. The extension M(L)/M(L’) is Galois, with Gal(M(L)/M(L’)) isomorph to L/aL’.
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MO is not for homework. – Felipe Voloch Feb 11 2011 at 21:10