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.
- Isogeny class
- Maximal curves
- Supersingular abelian threefold
Nart, E., & Ritzenthaler, C. (2008). Jacobians in isogeny classes of supersingular abelian threefolds in characteristic 2. Finite Fields and Their Applications, 14, 676-702. https://doi.org/10.1016/j.ffa.2007.09.006