Hyperelliptic curves over the rationals

class sage.schemes.hyperelliptic_curves.hyperelliptic_rational_field.HyperellipticCurve_rational_field(PP, f, h=None, names=None, genus=None)

Bases: HyperellipticCurve_generic, ProjectivePlaneCurve_field

lseries(prec=53)

Return the L-series of this hyperelliptic curve of genus 2.

EXAMPLES:

sage: x = polygen(QQ, 'x')
sage: C = HyperellipticCurve(x^2+x, x^3+x^2+1)
sage: C.lseries()
PARI L-function associated to Hyperelliptic Curve
over Rational Field defined by y^2 + (x^3 + x^2 + 1)*y = x^2 + x

matrix_of_frobenius(p, prec=20)