# Stored data for abelian variety isogeny class 2.71.a_act, downloaded from the LMFDB on 07 October 2026.
{"abvar_count": 4971, "abvar_counts": [4971, 24710841, 128100999744, 646009808058729, 3255243549205651851, 16409866135412288065536, 82721210695561233807550491, 416997655935737446666847298249, 2102085018129621403473011581737024, 10596610564645009123657611081819726201], "abvar_counts_str": "4971 24710841 128100999744 646009808058729 3255243549205651851 16409866135412288065536 82721210695561233807550491 416997655935737446666847298249 2102085018129621403473011581737024 10596610564645009123657611081819726201 ", "angle_corank": 2, "angle_rank": 0, "angles": [0.166666666666667, 0.833333333333333], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 72, "curve_counts": [72, 4900, 357912, 25421764, 1804229352, 128101715566, 9095120158392, 645753582069124, 45848500718449032, 3255243547401422500], "curve_counts_str": "72 4900 357912 25421764 1804229352 128101715566 9095120158392 645753582069124 45848500718449032 3255243547401422500 ", "curves": ["y^2=x^6+62*x^5+63*x^4+23*x^3+55*x^2+17*x+51", "y^2=9*x^6+66*x^5+52*x^4+6*x^3+70*x^2+59*x+9", "y^2=63*x^6+36*x^5+9*x^4+42*x^3+64*x^2+58*x+63", "y^2=13*x^6+43*x^5+41*x^4+68*x^3+21*x^2+35*x+13", "y^2=20*x^6+17*x^5+3*x^4+50*x^3+5*x^2+32*x+20", "y^2=15*x^6+24*x^5+70*x^4+28*x^3+33*x^2+66*x+15", "y^2=34*x^6+26*x^5+64*x^4+54*x^3+18*x^2+36*x+34", "y^2=12*x^6+26*x^5+49*x^4+17*x^3+28*x^2+46*x+12", "y^2=13*x^6+40*x^5+59*x^4+48*x^3+54*x^2+38*x+13", "y^2=33*x^6+16*x^5+64*x^4+23*x^3+53*x^2+40*x+33", "y^2=18*x^6+41*x^5+22*x^4+19*x^3+16*x^2+67*x+18", "y^2=54*x^6+27*x^5+25*x^4+29*x^3+61*x^2+13*x+54", "y^2=23*x^6+47*x^5+33*x^4+61*x^3+x^2+20*x+23"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 1, "dim2_factors": 1, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 4, "g": 2, "galois_groups": ["4T2"], "geom_dim1_distinct": 1, "geom_dim1_factors": 2, "geom_dim2_distinct": 0, "geom_dim2_factors": 0, "geom_dim3_distinct": 0, "geom_dim3_factors": 0, "geom_dim4_distinct": 0, "geom_dim4_factors": 0, "geom_dim5_distinct": 0, "geom_dim5_factors": 0, "geometric_center_dim": 1, "geometric_extension_degree": 6, "geometric_galois_groups": ["1T1"], "geometric_number_fields": ["1.1.1.1"], "geometric_splitting_field": "1.1.1.1", "geometric_splitting_polynomials": [[0, 1]], "group_structure_count": 1, "has_geom_ss_factor": true, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 13, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": true, "jacobian_count": 13, "label": "2.71.a_act", "max_divalg_dim": 1, "max_geom_divalg_dim": 4, "max_twist_degree": 24, "newton_coelevation": 0, "newton_elevation": 2, "noncyclic_primes": [], "number_fields": ["4.0.45369.1"], "p": 71, "p_rank": 0, "p_rank_deficit": 2, "poly": [1, 0, -71, 0, 5041], "poly_str": "1 0 -71 0 5041 ", "primitive_models": [], "q": 71, "real_poly": [1, 0, -213], "simple_distinct": ["2.71.a_act"], "simple_factors": ["2.71.a_actA"], "simple_multiplicities": [1], "singular_primes": ["2,F+V-7", "71,V-71,-2*F-V+142"], "slopes": ["1/2A", "1/2B", "1/2C", "1/2D"], "splitting_field": "4.0.45369.1", "splitting_polynomials": [[324, -18, -17, -1, 1]], "twist_count": 5, "twists": [["2.71.a_fm", "2.357911.a_bosxq", 3], ["2.71.a_ct", "2.25411681.oxu_gkvltb", 4], ["2.71.a_afm", "2.16409682740640811134241.aclusktprw_cgsgkjfspbarrpcyg", 12], ["2.71.a_a", "2.269277687648484922418719360310447236922646081.abndmygdvbjjddbkqe_wcifwenwlpuinjqfosneutebxjzrxxwg", 24]], "weak_equivalence_count": 4, "zfv_index": 284, "zfv_index_factorization": [[2, 2], [71, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 5041, "zfv_singular_count": 5, "zfv_singular_primes": ["2,F+V-7", "71,V-71,-2*F-V+142"]}