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arXiv · 1407.7892

Picard curves over Q with good reduction away from 3

Beth Malmskog·Christopher Rasmussen
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Abstract

Inspired by methods of N. P. Smart, we describe an algorithm to determine all Picard curves over Q with good reduction away from 3, up to Q-isomorphism. A correspondence between the isomorphism classes of such curves and certain quintic binary forms possessing a rational linear factor is established. An exhaustive list of integral models is determined, and an application to a question of Ihara is discussed.

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Beth Malmskog, Christopher Rasmussen. 2014-07-29. Picard curves over Q with good reduction away from 3. https://doi.org/10.1112/s1461157016000413

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