Magma version V2.30-1
1. residues modulo 7: -3 = 4 and -1/3 = 2 are squares, -1 = 6 is not: OK
possible #A(F_2) for an abelian surface A over F_2: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 25 ]
2. no abelian surface over F_2 has 63 | #A(F_2): OK
3. identities in Q(sqrt(-3)): u^2-u+1 = 0, S^2 = -1/3, T^2 = -3, (T) = (zeta_3 - 1): OK
4. L = Q(zeta_9)^+ = Q[x]/(x^3-3x+1) is cyclic cubic, unramified at 5, and 5 is inert: OK
j(162b1) = -140625/8
5. 162b1: conductor 162, non-CM, a_5 = 0, and E(L)_tors = Z/21 generated by (1-2a, 2-2a): OK
6. #A(F_5) = N(1 + 5 zeta^2) = 21, which is not divisible by 63: OK
ALL_CHECKS_PASSED