English

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 Q\mathbb{Q} 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 Q\mathbb{Q} of small conductor.

Keywords

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}
}

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34 pages