# Stored data for abelian variety isogeny class 2.73.ax_km, downloaded from the LMFDB on 19 December 2025.
{"abvar_count": 3900, "abvar_counts": [3900, 28485600, 151943828400, 806874559920000, 4297745938426297500, 22902034398956839526400, 122044995598654055016183900, 650377884379561414445603520000, 3465863728848181448580493461524400, 18469587767798460532997529385811340000], "abvar_counts_str": "3900 28485600 151943828400 806874559920000 4297745938426297500 22902034398956839526400 122044995598654055016183900 650377884379561414445603520000 3465863728848181448580493461524400 18469587767798460532997529385811340000 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.194368965322337, 0.323434683416109], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 51, "curve_counts": [51, 5345, 390582, 28412833, 2073129531, 151334136110, 11047396849827, 806460097550593, 58871586832250886, 4297625828694458225], "curve_counts_str": "51 5345 390582 28412833 2073129531 151334136110 11047396849827 806460097550593 58871586832250886 4297625828694458225 ", "curves": ["y^2=40*x^6+61*x^5+68*x^4+46*x^3+12*x^2+18*x+26", "y^2=11*x^6+25*x^5+33*x^4+39*x^3+41*x^2+55*x+20", "y^2=18*x^6+47*x^5+56*x^4+51*x^3+24*x^2+7*x+46", "y^2=19*x^6+58*x^5+25*x^4+16*x^3+64*x^2+7*x+33", "y^2=22*x^6+36*x^5+25*x^4+20*x^3+56*x^2+9*x+65", "y^2=31*x^6+57*x^5+37*x^4+61*x^3+71*x^2+69*x+61", "y^2=15*x^6+47*x^4+12*x^3+15*x^2+6*x+60", "y^2=15*x^6+27*x^5+51*x^4+38*x^3+37*x^2+72*x+50", "y^2=30*x^6+36*x^5+18*x^4+17*x^3+9*x^2+29*x+50", "y^2=19*x^6+27*x^5+47*x^4+37*x^3+42*x^2+4*x+43", "y^2=28*x^6+71*x^5+8*x^4+59*x^3+17*x^2+69*x+20", "y^2=13*x^6+23*x^5+44*x^4+31*x^3+44*x^2+7*x+15", "y^2=37*x^6+67*x^5+6*x^4+60*x^3+57*x^2+45*x+62", "y^2=43*x^6+36*x^5+48*x^4+4*x^3+53*x^2+58*x+5", "y^2=54*x^6+20*x^5+69*x^4+68*x^3+36*x^2+70*x+62", "y^2=41*x^6+54*x^5+69*x^4+38*x^3+52*x^2+45*x+8", "y^2=26*x^6+3*x^5+36*x^4+25*x^3+34*x^2+72*x+16", "y^2=41*x^6+72*x^5+x^4+15*x^2+10*x+21", "y^2=27*x^6+44*x^5+65*x^4+62*x^3+28*x^2+27*x+47", "y^2=71*x^6+19*x^5+8*x^4+2*x^3+35*x^2+68*x+10", "y^2=50*x^6+51*x^5+33*x^4+49*x^3+30*x^2+29*x+63", "y^2=16*x^6+70*x^5+47*x^4+44*x^3+17*x^2+65*x+29", "y^2=40*x^6+56*x^5+32*x^4+56*x^3+56*x^2+66*x+8", "y^2=51*x^6+58*x^5+22*x^4+47*x^3+46*x^2+69*x+19", "y^2=38*x^6+16*x^5+17*x^4+63*x^3+29*x^2+x+21", "y^2=9*x^6+13*x^5+64*x^4+56*x^3+72*x+63", "y^2=22*x^6+53*x^5+2*x^3+29*x^2+20*x+32", "y^2=34*x^6+43*x^5+12*x^4+35*x^3+13*x^2+46*x+47", "y^2=59*x^6+32*x^5+43*x^4+38*x^3+52*x^2+16*x+56", "y^2=2*x^6+63*x^5+36*x^4+55*x^3+30*x^2+7*x+43", "y^2=31*x^6+52*x^5+31*x^4+34*x^3+32*x^2+13*x+64", "y^2=72*x^6+30*x^5+40*x^4+38*x^3+54*x^2+11*x+70", "y^2=56*x^6+21*x^5+42*x^4+46*x^3+22*x^2+35*x+45", "y^2=53*x^6+38*x^5+6*x^4+35*x^3+49*x^2+42*x+18", "y^2=27*x^6+56*x^5+7*x^4+25*x^3+19*x^2+35*x+33", "y^2=66*x^6+59*x^5+10*x^4+10*x^3+26*x^2+29*x+54"], "dim1_distinct": 2, "dim1_factors": 2, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 8, "g": 2, "galois_groups": ["2T1", "2T1"], "geom_dim1_distinct": 2, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.24.1", "2.0.211.1"], "geometric_splitting_field": "4.0.25644096.1", "geometric_splitting_polynomials": [[2215, -118, 119, -2, 1]], "group_structure_count": 4, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 36, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 36, "label": "2.73.ax_km", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2, 5], "number_fields": ["2.0.24.1", "2.0.211.1"], "p": 73, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 4], [1, 7, 1, 4], [1, 11, 1, 4], [2, 11, 1, 3]], "poly": [1, -23, 272, -1679, 5329], "poly_str": "1 -23 272 -1679 5329 ", "primitive_models": [], "principal_polarization_count": 54, "q": 73, "real_poly": [1, -23, 126], "simple_distinct": ["1.73.ao", "1.73.aj"], "simple_factors": ["1.73.aoA", "1.73.ajA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,-5*F-3", "5,20*F-V+6", "5,-4*F-6"], "size": 234, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.25644096.1", "splitting_polynomials": [[2215, -118, 119, -2, 1]], "twist_count": 4, "twists": [["2.73.af_u", "2.5329.p_kyy", 2], ["2.73.f_u", "2.5329.p_kyy", 2], ["2.73.x_km", "2.5329.p_kyy", 2]], "weak_equivalence_count": 8, "zfv_index": 50, "zfv_index_factorization": [[2, 1], [5, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 96, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 20256, "zfv_singular_count": 6, "zfv_singular_primes": ["2,-5*F-3", "5,20*F-V+6", "5,-4*F-6"]}