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Some remarks on the Picard curves over a finite field

✍ Scribed by Yoh Takizawa

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
127 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In this paper we study the Newton polygon of the L ‐polynomial L (t) associate to the Picard curves

y^3^ = x^4^ – 1, y^3^ = x^4^ – x

defined over a finite field 𝔽~p~ . In the former case we get a complete classification. In the latter case we obtained a partial result.

As a consequence of our result we obtain a criterion to find a supersingular Picard curves for the above two cases. Our main results are stated in Theorems 3.1 and 4.1. (Β© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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