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Elliptic curves over totally real quartic fields not containing are modular
Josha Box
We prove that every elliptic curve defined over a totally real number field of degree 4 not containing is modular. To this end, we study the quartic points on four modul…
Models for quotients of modular curves
Josha Box
We describe an algorithm for computing a $\Q$-rational model for the quotient of a modular curve by an automorphism group, under mild assumptions on the curve and the automorphisms…
Bounding integral points on the Siegel modular variety A_2(2)
Josha Box, Samuel le Fourn
We determine two explicit upper bounds for the stable Faltings height of principally polarised abelian surfaces over number fields corresponding to S-integral points on the Siegel…
Quadratic points on modular curves with infinite Mordell--Weil group
Josha Box
Bruin--Najman and Ozman--Siksek have recently determined the quadratic points on all modular curves of genus 2, 3, 4, and 5 whose Mordell--Weil group has rank 0. In this p…