Families of supersingular curves in characteristic 2
Jasper Scholten, Hui June Zhu · Mathematical Research Letters · 2002
This paper determines normal forms of all hyperelliptic supersingular curves of genus g over an algebraically closed field F of characteristic 2 for 1 ≤ g ≤ 8.We also show that every hyperelliptic supersingular curve of genus 9 over F has an equation y 2y = x 19 + c 8 x 9 + c 3 x for some c ∈ F 2 .Consequently, the paper determines the dimensions of the open locus of hyperelliptic supersingular curves of genus g ≤ 9 over F 2 .