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

中文翻译：

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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$\mathbb{问}$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$\mathbb{问}$ 小导体。