Trisection for supersingular genur 2 curves in characteristic 2
Issue date
2014Suggested citation
Miret, Josep M. (Josep Maria);
Pujolàs Boix, Jordi;
Thériault, Nicolas;
.
(2014)
.
Trisection for supersingular genur 2 curves in characteristic 2.
Advances in Mathematics of Communications, 2014, vol. 8, núm. 4, 375-387.
https://doi.org/10.3934/amc.2014.8.375.
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By reversing reduction in divisor class arithmetic we provide efficient trisection algorithms for Jacobians of supersingular genus 2 curves over finite fields of characteristic 2. With our technique we obtain new results for these Jacobians: we show how to find their 3-torsion subgroup, we prove there is none with 3-torsion subgroup of rank 3 and we prove their the maximal 3-power order subgroup is isomorphic to either Z/3^vZ or (Z/3^{v/2}Z)^2 or (Z/3^{v/4}Z)^4, where v is the 3-adic valuation v3(#Jac(C)(F2^m}). Ours are the first trisection formulae available in literature.