Using an analogue of Serre’s open image theorem for elliptic curves with complex multiplication, one can associate to each CM elliptic curve E defnied over a number feild F a natural number I(E/F) which describes how big the image of the Galois representation associated to E is. We show how one can compute I(E/F), using a closed formula that we obtain from the classical theory of complex multiplication.
How big is the image of the Galois representations attached to CM elliptic curves?
Pengo, Riccardo
2022-01-01
Abstract
Using an analogue of Serre’s open image theorem for elliptic curves with complex multiplication, one can associate to each CM elliptic curve E defnied over a number feild F a natural number I(E/F) which describes how big the image of the Galois representation associated to E is. We show how one can compute I(E/F), using a closed formula that we obtain from the classical theory of complex multiplication.File in questo prodotto:
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