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- W4297947319 abstract "The aim of the inverse Galois problem is to find extensions of a given field whose Galois group is isomorphic to a given group. In this article, we are interested in subgroups of GL(2,Z/nZ) where n is an integer. We know that, in general, we can realize these groups as the Galois group of a given number field, using the torsion points on an elliptic curve. Specifically, a theorem of Reverter and Vila (2000) gives, for each prime n, a polynomial, depending on an elliptic curve, whose Galois group is GL(2,Z/nZ). In this article, we generalize this theorem in several directions, in particular for n non necessarily prime. We also determine a minimum for the valuations of the coefficients of the polynomials arising in our construction, depending only on n." @default.
- W4297947319 created "2022-10-01" @default.
- W4297947319 creator A5021881092 @default.
- W4297947319 date "2022-09-27" @default.
- W4297947319 modified "2023-10-13" @default.
- W4297947319 title "Polynomials realizing images of Galois representations of an elliptic curve" @default.
- W4297947319 doi "https://doi.org/10.7169/facm/2106" @default.
- W4297947319 hasPublicationYear "2022" @default.
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