Conductor and discriminant of Picard curves
Number Theory
2020-05-06 v1
Abstract
We describe normal forms and minimal models of Picard curves, discussing various arithmetic aspects of these. We determine all so-called special Picard curves over with good reduction outside 2 and 3, and use this to determine the smallest possible conductor a special Picard curve may have. We also collect a database of Picard curves over of small conductor.
Cite
@article{arxiv.1902.09624,
title = {Conductor and discriminant of Picard curves},
author = {Irene I. Bouw and Angelos Koutsianas and Jeroen Sijsling and Stefan Wewers},
journal= {arXiv preprint arXiv:1902.09624},
year = {2020}
}
Comments
34 pages