On uniform lower bound of the Galois images associated to elliptic curves

Details On uniform lower bound of the Galois images associated to elliptic curves On uniform lower bound of the Galois images associated to elliptic curves

2007-03-23

arxiv.org/abs/math/0703686v1

Mathematics

Number Theory

41 pages

Scientific paper

Let p be a prime and K be a number field. Let rho_{E,p}:G_K \longrightarrow Aut(T_p E)\cong GL_2(Z_p) be the Galois representation given by the Galois action on the p-adic Tate module of an elliptic curve E over K. Serre showed that the image of rho_{E,p} is open if E has no complex multiplication. For an elliptic curve E over K whose j-invariant does not appear in an exceptional finite set, we give an explicit uniform lower bound of the size of the image of rho_{E,p}.

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