Magma V2.30-1
number of Weil polynomials over F_2 (abelian surfaces): 35
values of P(1): [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 25 ]
Weil polynomials with 13 | P(1): [
T^4 + 2*T^3 + 2*T^2 + 4*T + 4
]
P0 = T^4 + 2T^3 + 2T^2 + 4T + 4 is irreducible, P0(1) = 13, root field = Q(zeta_12)
quadratic subfields of Q(zeta_12): discriminants { -4, -3, 12 }
Q(sqrt -1): 4 roots of unity; 13 splits: true
Q(sqrt -3): 6 roots of unity; 13 splits: true
[ 0, 0, 0, -1, 0 ]: conductor 32, CM discriminant -4, a_13 = 6
[ 0, 0, 0, 0, 1 ]: conductor 36, CM discriminant -3, a_13 = 2
ALL_CHECKS_PASSED