58 citations · 62 across the 10 of their papers we have counts for
12 papers
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.
Moduli-friendly Eisenstein series over the p-adics and the computation of modular Galois representations
Nicolas Mascot
We show how our p-adic method to compute Galois representations occurring in the torsion of Jacobians of algebraic curves can be adapted to modular curves. The main ingredient is t…
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…
Hensel-lifting torsion points on Jacobians and Galois representations
Nicolas Mascot
Let be a mod Galois representation. We show how to compute , given the characteristic polynomial of the image of the Frobenius at one prime and a curve whose…
Rigorous computation of the endomorphism ring of a Jacobian
Edgar Costa, Nicolas Mascot, Jeroen Sijsling +1
We describe several improvements to algorithms for the rigorous computation of the endomorphism ring of the Jacobian of a curve defined over a number field.
Companion forms and explicit computation of PGL2 number fields with very little ramification
Nicolas Mascot
In previous works, we described algorithms to compute the number field cut out by the mod ell representation attached to a modular form of level N=1. In this article, we explain ho…
Certification of modular Galois representations
Nicolas Mascot
We show how the output of the algorithm to compute modular Galois representations described in our previous article can be certified. We have used this process to compute certified…
Computing modular Galois representations
Nicolas Mascot
We compute modular Galois representations associated with a newform , and study the related problem of computing the coefficients of modulo a small prime . To this end…