Hyperelliptic curves, Cartier-Manin matrices and Legendre polynomials are centrosymmetric and, therefore, it’
s enough to compute
a half of coefficients to compute the matrix. Moreover
On the distribution of orders of Frobenius action on l-torsion of abelian surfacesThe computation of the order of Frobenius action on the ^-torsion is
a part of Schoof — Elkies
Counting points on hyperelliptic curves of type y2 = x2g +1 + axg +1 + bx1 the finite field Fq, q = pn, p > 2. For the case of g = 3 or 4, p { 4g and b is
a 4g-root, we provide