Abstract
We determine the isogeny classes of supersingular abelian threefolds over F2n containing the Jacobian of a genus 3 curve. In particular, we prove that for even n > 6 there always exist a maximal and a minimal curves of genus 3 over F2n. The methods provide an explicit construction of supersingular curves of genus 3 with Jacobian in a prescribed isogeny class. © 2007 Elsevier Inc. All rights reserved.
Original language | English |
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Pages (from-to) | 676-702 |
Journal | Finite Fields and Their Applications |
Volume | 14 |
DOIs | |
Publication status | Published - 1 Jul 2008 |
Keywords
- Curve
- Isogeny class
- Jacobian
- Maximal curves
- Supersingular abelian threefold