A file with all genus 4 curves over F_2, up-to-isomorphism. Also the magma file used to compute it.
The file CurvesGenus4p2ModuloIso.magma contains the magma code used to compute the results. Also some computations concerning some of the data.
The file ListCurvesGenus4p2.txt contains 3 lists:
-
the first one is formed by list N containing the points over
$F_{2^r}$ for$r=1,2,3,4$ , which determine the jacobian up to isogeny. -
The second list H contains lists formed by list of the form [p,q], where p and q are polynomials in x over
$F_2$ ; they correspond to hyperelliptic curves with equation
y^2+q*y= p
in such a way that H[i][j] is a curve with number of points N[i].
- The third list C contains lists formed by lists of two polynomials
$f$ and$g$ in$F_2[X,Y,Z,T]$ , of degre 2 and 3 respectively, such that the projective curve with canonical equations f=0, g=0 C[i][j] is a curve with number of points N[i].
The file TheCurvesGenus4p2.magma contains the same data and neccessary to load the file to Magma in ordre to use the data. So it defines the field K, the variable x and the projective space P<X,Y,Z,T>:=ProjectiveSpace(K,3);