# Stored data for abelian variety isogeny class 2.71.ak_bd, downloaded from the LMFDB on 15 July 2026.
{"abvar_count": 4351, "abvar_counts": [4351, 25196641, 127293395524, 645542200652329, 3255248871690942751, 16409538992709615448336, 82721157759903909406933231, 416997634976125385191491464649, 2102084997077942155428191732383684, 10596610564673337880597545082778071201], "abvar_counts_str": "4351 25196641 127293395524 645542200652329 3255248871690942751 16409538992709615448336 82721157759903909406933231 416997634976125385191491464649 2102084997077942155428191732383684 10596610564673337880597545082778071201 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.0355444598469552, 0.631122206819712], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 62, "curve_counts": [62, 5000, 355652, 25403364, 1804232302, 128099161766, 9095114338162, 645753549611524, 45848500259291612, 3255243547410125000], "curve_counts_str": "62 5000 355652 25403364 1804232302 128099161766 9095114338162 645753549611524 45848500259291612 3255243547410125000 ", "curves": ["y^2=28*x^6+30*x^5+61*x^4+9*x^3+4*x^2+22*x+51", "y^2=12*x^6+13*x^5+64*x^4+55*x^3+49*x^2+x+13", "y^2=25*x^6+70*x^5+54*x^4+6*x^3+2*x^2+45*x+62", "y^2=51*x^6+65*x^5+32*x^4+44*x^3+30*x^2+4*x+56", "y^2=59*x^6+30*x^5+13*x^4+3*x^3+47*x^2+50*x+58", "y^2=69*x^6+19*x^5+38*x^4+61*x^3+22*x^2+45*x+32", "y^2=30*x^6+52*x^5+24*x^4+69*x^3+45*x^2+11", "y^2=55*x^6+28*x^5+55*x^4+27*x^3+19*x^2+36", "y^2=31*x^6+67*x^5+14*x^4+58*x^3+28*x^2+6*x+12", "y^2=13*x^6+5*x^5+69*x^4+24*x^3+19*x^2+55*x+7", "y^2=33*x^6+28*x^5+60*x^4+18*x^3+5*x^2+19*x+66", "y^2=34*x^6+46*x^5+7*x^4+42*x^3+55*x^2+52*x+20", "y^2=52*x^6+46*x^5+50*x^4+21*x^3+17*x^2+38*x+66", "y^2=10*x^6+64*x^5+35*x^4+14*x^3+4*x^2+55*x+27", "y^2=x^6+42*x^5+8*x^4+21*x^3+15*x^2+53*x+16", "y^2=60*x^6+67*x^5+68*x^4+12*x^3+28*x^2+24*x+4", "y^2=14*x^6+42*x^5+24*x^4+50*x^3+28*x^2+x+32", "y^2=69*x^6+13*x^5+38*x^4+40*x^3+9*x^2+38*x+62", "y^2=23*x^6+41*x^5+55*x^4+26*x^3+39*x^2+59*x+3", "y^2=7*x^6+49*x^5+61*x^4+14*x^3+61*x^2+20*x+61", "y^2=54*x^6+12*x^5+65*x^4+16*x^3+21*x^2+30*x+20", "y^2=43*x^6+14*x^5+29*x^4+63*x^3+49*x^2+52*x+10", "y^2=47*x^6+20*x^5+39*x^4+40*x^3+27*x^2+60*x+62", "y^2=25*x^6+4*x^5+28*x^4+45*x^3+43*x^2+9*x+44", "y^2=55*x^6+20*x^5+51*x^4+22*x^3+68*x^2+3*x+12", "y^2=33*x^6+25*x^5+23*x^4+12*x^3+66*x^2+19*x+49", "y^2=19*x^6+61*x^5+27*x^4+25*x^3+49*x^2+53*x+23", "y^2=67*x^6+46*x^5+40*x^4+60*x^3+13*x^2+2*x+43", "y^2=68*x^6+34*x^5+13*x^4+44*x^3+36*x^2+61*x+48", "y^2=26*x^6+28*x^5+2*x^4+17*x^3+36*x^2+38*x+14", "y^2=69*x^6+29*x^5+26*x^4+13*x^3+2*x^2+22*x+32", "y^2=34*x^6+57*x^5+3*x^4+17*x^3+34*x^2+6*x+20", "y^2=30*x^6+39*x^5+67*x^4+63*x^3+24*x^2+20*x+31", "y^2=34*x^6+38*x^5+59*x^4+40*x^3+4*x^2+66*x+1", "y^2=66*x^6+11*x^5+41*x^4+20*x^3+x^2+50*x+19", "y^2=59*x^6+69*x^5+30*x^4+45*x^3+31*x^2+43*x+54", "y^2=47*x^6+58*x^5+57*x^4+9*x^3+46*x^2+24*x+13", "y^2=15*x^6+69*x^5+11*x^4+51*x^3+8*x^2+17*x+63", "y^2=16*x^6+18*x^5+29*x^4+15*x^3+5*x^2+50*x+62", "y^2=67*x^6+57*x^5+51*x^4+6*x^3+46*x^2+35*x+34"], "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": 2, "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": 3, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.184.1"], "geometric_splitting_field": "2.0.184.1", "geometric_splitting_polynomials": [[46, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 40, "is_cyclic": true, "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.ak_bd", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.304704.5"], "p": 71, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -10, 29, -710, 5041], "poly_str": "1 -10 29 -710 5041 ", "primitive_models": [], "q": 71, "real_poly": [1, -10, -113], "simple_distinct": ["2.71.ak_bd"], "simple_factors": ["2.71.ak_bdA"], "simple_multiplicities": [1], "singular_primes": ["29,2*F+43*V-421"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.304704.5", "splitting_polynomials": [[2116, 0, -46, 0, 1]], "twist_count": 6, "twists": [["2.71.k_bd", "2.5041.abq_aewb", 2], ["2.71.u_ji", "2.357911.adiy_ejjve", 3], ["2.71.au_ji", "2.128100283921.aclvzw_ctclemcwc", 6], ["2.71.a_bq", "2.128100283921.aclvzw_ctclemcwc", 6], ["2.71.k_bd", "2.128100283921.aclvzw_ctclemcwc", 6], ["2.71.a_abq", "2.16409682740640811134241.aoplnlaim_vpzwjevlzenwckfm", 12]], "weak_equivalence_count": 2, "zfv_index": 29, "zfv_index_factorization": [[29, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 841, "zfv_singular_count": 2, "zfv_singular_primes": ["29,2*F+43*V-421"]}