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Conductor and discriminant of Picard curves
Journal of the London Mathematical Society ( IF 1.0 ) Pub Date : 2020-04-29 , DOI: 10.1112/jlms.12323 Irene I. Bouw 1 , Angelos Koutsianas 2 , Jeroen Sijsling 1 , Stefan Wewers 1
Journal of the London Mathematical Society ( IF 1.0 ) Pub Date : 2020-04-29 , DOI: 10.1112/jlms.12323 Irene I. Bouw 1 , Angelos Koutsianas 2 , Jeroen Sijsling 1 , Stefan Wewers 1
Affiliation
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.
中文翻译:
皮卡德曲线的导体和判别
我们描述了Picard曲线的范式和最小模型,并讨论了这些曲线的各种算术方面。我们确定所有所谓的特殊皮卡德曲线在2和3以外具有良好的折减率,并用它来确定特殊的Picard曲线可能具有的最小导体。我们还收集了皮卡德曲线的数据库 小导体。
更新日期:2020-04-29
中文翻译:
皮卡德曲线的导体和判别
我们描述了Picard曲线的范式和最小模型,并讨论了这些曲线的各种算术方面。我们确定所有所谓的特殊皮卡德曲线在2和3以外具有良好的折减率,并用它来确定特殊的Picard曲线可能具有的最小导体。我们还收集了皮卡德曲线的数据库 小导体。