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Genus2Euler

Code and data associated to the paper Computing Euler factors of genus 2 curves at odd primes of almost good reduction, by Céline Maistret and Andrew V. Sutherland.

  • The package file genus2euler.m implements Algorithm 7 of the paper as a Magma intrinsic Genus2AlmostGoodEulerFactor.
  • The text file EulerFactorHardCases.txt lists tuples case:p:[f0,...,f6],[a1,a2]:t1:t2:t3, where case= 1,2,3,4 indicates the type 1, 2a, 2b, 4 defined in the paper, p is an odd prime of almost good reduction for the genus 2 hyperelliptic curve y^2=f(x) defined by the coefficients f0,...,f6, a1 and a2 are the linear and quadratic coefficients of the L-polynomial Lp(C,T), and t1,t2,t3 are running times (in seconds) for the existing Magma intrinsic EulerFactor, the new Magma intrinsic AlmostGoodEulerFactor, and our low level C implementation, respectively.
  • The text file EulerFactorFailureCases.txt lists 489 tuples in the format above where the existing Magma intrinsic EulerFactor failed to terminated (here t1 is capped at 8 hours).