1 citations · 2 across the 4 of their papers we have counts for
5 papers
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…
Cubic and quartic points on modular curves using generalised symmetric Chabauty
Josha Box, Stevan Gajović, Pip Goodman
Answering a question of Zureick-Brown, we determine the cubic points on the modular curves for as well as the quartic points on . To…
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…