greenberg 11a -- rank over Q(zeta

M = ModularSymbols(11,2)

for eps in DirichletGroup(5): N = M.change_ring(eps.base_ring()) s = N.twisted_winding_element(0, eps) phi = N.cuspidal_submodule().rational_period_mapping() print phi(s)

(-5, 0)
(5*zeta4, -2*zeta4)
(25, 0)
(-5*zeta4, 2*zeta4)

(-5, 0)
(5*zeta4, -2*zeta4)
(25, 0)
(-5*zeta4, 2*zeta4)

E = EllipticCurve('11a').change_ring(CyclotomicField(5))

E.torsion_order()

greenberg 11a -- rank over Q(zeta_5)

585 days ago by wstein