7 papers · 1 filter
Equationless quadratic Chabauty for non-split Cartan modular curves
Sachi Hashimoto, Guido Maria Lido, Davide Lombardo +2
The aim of this article is to describe an equationless method for determining the rational points on the non-split Cartan curve of prime level .…
Explicit computation of Galois representations occurring in families of curves
Nicolas Mascot
We extend our method to compute division polynomials of Jacobians of curves over Q to curves over Q(t), in view of computing mod ell Galois representations occurring in the étale c…
A method to prove that a modular Galois representation has large image
Nicolas Mascot
Let be a mod Galois representation attached to a newform . Explicit methods are sometimes able to determine the image of , or even the number field cut out by ,…
Computing the trace of an algebraic point on an elliptic curve
Nicolas Mascot, Denis Simon
We present a simple and efficient algorithm to compute the sum of the algebraic conjugates of a point on an elliptic curve.
A Prym variety with everywhere good reduction over
Nicolas Mascot, Jeroen Sijsling, John Voight
We compute an equation for a modular abelian surface that has everywhere good reduction over the quadratic field and that does not admit a principal…
Explicit computation of a Galois representation attached to an eigenform over SL3 from the H2 étale of a surface
Nicolas Mascot
We sketch a method to compute mod Galois representations contained in the H2 étale of surfaces. We apply this method to the case of a representation with values in GL(3,9) a…