TY - UNPB
T1 - Cubic and quartic points on modular curves using generalised symmetric Chabauty
AU - Box, Josha
AU - Gajovic, Stevan
AU - Goodman, Pip
PY - 2021/11/23
Y1 - 2021/11/23
N2 - Answering a question of Zureick-Brown, we determine the cubic points on the modular curves X0(N) for N∈{53,57,61,65,67,73} as well as the quartic points on X0(65). To do so, we develop a "partially relative" symmetric Chabauty method. Our results generalise current symmetric Chabauty theorems, and improve upon them by lowering the involved prime bound. For our curves a number of novelties occur. We prove a "higher order" Chabauty theorem to deal with these cases. Finally, to study the isolated quartic points on X0(65), we rigorously compute the full rational Mordell--Weil group of its Jacobian.
AB - Answering a question of Zureick-Brown, we determine the cubic points on the modular curves X0(N) for N∈{53,57,61,65,67,73} as well as the quartic points on X0(65). To do so, we develop a "partially relative" symmetric Chabauty method. Our results generalise current symmetric Chabauty theorems, and improve upon them by lowering the involved prime bound. For our curves a number of novelties occur. We prove a "higher order" Chabauty theorem to deal with these cases. Finally, to study the isolated quartic points on X0(65), we rigorously compute the full rational Mordell--Weil group of its Jacobian.
U2 - 10.48550/arXiv.2102.08236
DO - 10.48550/arXiv.2102.08236
M3 - Preprint
BT - Cubic and quartic points on modular curves using generalised symmetric Chabauty
PB - arXiv
ER -