# Stored data for abelian variety isogeny class 2.71.a_aen, downloaded from the LMFDB on 04 April 2026.
{"abvar_count": 4925, "abvar_counts": [4925, 24255625, 128100451700, 645570275205625, 3255243554588223125, 16409725725744032890000, 82721210695578972486010325, 416997671952016942325592755625, 2102085018129621252021641481941300, 10596610599688169988285978944784765625], "abvar_counts_str": "4925 24255625 128100451700 645570275205625 3255243554588223125 16409725725744032890000 82721210695578972486010325 416997671952016942325592755625 2102085018129621252021641481941300 10596610599688169988285978944784765625 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.0958846096256865, 0.904115390374314], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 72, "curve_counts": [72, 4808, 357912, 25404468, 1804229352, 128100619478, 9095120158392, 645753606871588, 45848500718449032, 3255243558166565048], "curve_counts_str": "72 4808 357912 25404468 1804229352 128100619478 9095120158392 645753606871588 45848500718449032 3255243558166565048 ", "curves": ["y^2=10*x^6+3*x^5+49*x^4+28*x^3+39*x^2+6*x+18", "y^2=70*x^6+21*x^5+59*x^4+54*x^3+60*x^2+42*x+55", "y^2=47*x^6+20*x^5+37*x^4+21*x^3+42*x^2+50*x+61", "y^2=65*x^6+21*x^5+45*x^4+21*x^3+5*x^2+12*x+22", "y^2=29*x^6+5*x^5+31*x^4+5*x^3+35*x^2+13*x+12", "y^2=29*x^6+31*x^5+9*x^4+42*x^3+5*x^2+2*x+19", "y^2=27*x^6+48*x^5+61*x^4+7*x^3+40*x^2+28*x+55", "y^2=47*x^6+52*x^5+x^4+49*x^3+67*x^2+54*x+30", "y^2=31*x^6+43*x^5+24*x^4+70*x^3+55*x^2+48*x+5", "y^2=27*x^6+62*x^5+51*x^4+44*x^3+10*x^2+46*x+5", "y^2=60*x^6+52*x^5+70*x^4+50*x^3+49*x^2+60*x+33", "y^2=20*x^6+12*x^5+22*x^4+8*x^3+11*x^2+25*x+67", "y^2=69*x^6+13*x^5+12*x^4+56*x^3+6*x^2+33*x+43", "y^2=27*x^6+29*x^5+60*x^4+46*x^3+61*x^2+49*x+11", "y^2=47*x^6+61*x^5+65*x^4+38*x^3+x^2+59*x+6", "y^2=53*x^6+67*x^5+24*x^4+25*x^3+42*x^2+53*x+63", "y^2=16*x^6+43*x^5+26*x^4+33*x^3+10*x^2+16*x+15", "y^2=6*x^6+30*x^5+62*x^4+4*x^3+48*x^2+25*x+22", "y^2=42*x^6+68*x^5+8*x^4+28*x^3+52*x^2+33*x+12", "y^2=44*x^6+50*x^5+34*x^4+33*x^3+62*x^2+60*x+21", "y^2=24*x^6+66*x^5+25*x^4+18*x^3+8*x^2+65*x+5", "y^2=22*x^6+62*x^5+70*x^4+4*x^3+9*x^2+52*x+7", "y^2=12*x^6+8*x^5+64*x^4+28*x^3+63*x^2+9*x+49", "y^2=5*x^6+5*x^5+34*x^4+41*x^3+48*x^2+43*x+44", "y^2=35*x^6+35*x^5+25*x^4+3*x^3+52*x^2+17*x+24", "y^2=12*x^6+56*x^5+57*x^4+35*x^3+31*x^2+11*x+14", "y^2=13*x^6+37*x^5+44*x^4+32*x^3+4*x^2+6*x+27", "y^2=11*x^6+51*x^5+24*x^4+36*x^3+57*x^2+25*x+21", "y^2=6*x^6+2*x^5+26*x^4+39*x^3+44*x^2+33*x+5", "y^2=46*x^6+23*x^4+22*x^3+42*x^2+44*x+56", "y^2=29*x^6+55*x^5+32*x^4+19*x^3+28*x^2+55*x+62", "y^2=32*x^6+9*x^5+58*x^4+19*x^3+23*x^2+50*x+41", "y^2=11*x^6+63*x^5+51*x^4+62*x^3+19*x^2+66*x+3", "y^2=4*x^6+24*x^5+22*x^4+64*x^3+38*x^2+15*x+27", "y^2=52*x^6+16*x^5+67*x^4+8*x^3+64*x^2+12*x+39", "y^2=9*x^6+41*x^5+43*x^4+56*x^3+22*x^2+13*x+60", "y^2=67*x^6+24*x^5+54*x^4+61*x^3+23*x^2+29*x+27", "y^2=43*x^6+26*x^5+23*x^4+x^3+19*x^2+61*x+47", "y^2=24*x^6+27*x^5+28*x^4+48*x^3+30*x^2+11*x+41", "y^2=26*x^6+47*x^5+54*x^4+52*x^3+68*x^2+6*x+3"], "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": 2, "geometric_extension_degree": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.259.1"], "geometric_splitting_field": "2.0.259.1", "geometric_splitting_polynomials": [[65, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 40, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 40, "label": "2.71.a_aen", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [5], "number_fields": ["4.0.1073296.4"], "p": 71, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 2], [1, 13, 1, 8], [1, 37, 1, 4]], "poly": [1, 0, -117, 0, 5041], "poly_str": "1 0 -117 0 5041 ", "primitive_models": [], "principal_polarization_count": 52, "q": 71, "real_poly": [1, 0, -259], "simple_distinct": ["2.71.a_aen"], "simple_factors": ["2.71.a_aenA"], "simple_multiplicities": [1], "singular_primes": ["5,29*F-17*V+2", "5,F^2+2*F+2"], "size": 52, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.1073296.4", "splitting_polynomials": [[4225, 0, -129, 0, 1]], "twist_count": 6, "twists": [["2.71.ak_gl", "2.25411681.akrm_fjrwsp", 4], ["2.71.a_en", "2.25411681.akrm_fjrwsp", 4], ["2.71.k_gl", "2.25411681.akrm_fjrwsp", 4], ["2.71.af_abu", "2.16409682740640811134241.ceulzxrrw_byoykrybaihznyyyg", 12], ["2.71.f_abu", "2.16409682740640811134241.ceulzxrrw_byoykrybaihznyyyg", 12]], "weak_equivalence_count": 4, "zfv_index": 25, "zfv_index_factorization": [[5, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 32, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 625, "zfv_singular_count": 4, "zfv_singular_primes": ["5,29*F-17*V+2", "5,F^2+2*F+2"]}