# Stored data for abelian variety isogeny class 2.71.a_ew, downloaded from the LMFDB on 08 June 2026.
{"abvar_count": 5168, "abvar_counts": [5168, 26708224, 128100378800, 645459145068544, 3255243548357732528, 16409707048703489440000, 82721210695552551368821808, 416997645398647394938737721344, 2102085018129621276168390021393200, 10596610559124641311491431249589270784], "abvar_counts_str": "5168 26708224 128100378800 645459145068544 3255243548357732528 16409707048703489440000 82721210695552551368821808 416997645398647394938737721344 2102085018129621276168390021393200 10596610559124641311491431249589270784 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.423719104037511, 0.576280895962489], "center_dim": 4, "cohen_macaulay_max": 3, "curve_count": 72, "curve_counts": [72, 5294, 357912, 25400094, 1804229352, 128100473678, 9095120158392, 645753565751614, 45848500718449032, 3255243545705583854], "curve_counts_str": "72 5294 357912 25400094 1804229352 128100473678 9095120158392 645753565751614 45848500718449032 3255243545705583854 ", "curves": ["y^2=46*x^6+36*x^5+48*x^4+8*x^3+44*x^2+47*x+42", "y^2=38*x^6+39*x^5+52*x^4+56*x^3+24*x^2+45*x+10", "y^2=43*x^6+4*x^5+57*x^4+69*x^3+36*x^2+66*x+70", "y^2=59*x^6+45*x^5+55*x^4+45*x^3+55*x^2+45*x+59", "y^2=58*x^6+31*x^5+30*x^4+31*x^3+30*x^2+31*x+58", "y^2=16*x^6+57*x^5+55*x^4+19*x^3+52*x+34", "y^2=41*x^6+44*x^5+30*x^4+62*x^3+9*x+25", "y^2=50*x^6+56*x^5+70*x^4+42*x^3+25*x^2+44*x+20", "y^2=2*x^6+56*x^5+36*x^4+16*x^3+50*x^2+23*x+1", "y^2=14*x^6+37*x^5+39*x^4+41*x^3+66*x^2+19*x+7", "y^2=17*x^6+44*x^5+8*x^4+61*x^3+59*x^2+28*x+58", "y^2=21*x^6+36*x^5+19*x^4+69*x^3+49*x^2+13*x+14", "y^2=32*x^6+66*x^5+47*x^4+61*x^3+21*x^2+48*x+34", "y^2=11*x^6+36*x^5+45*x^4+x^3+5*x^2+52*x+25", "y^2=22*x^6+24*x^5+16*x^4+24*x^3+60*x^2+7*x+69", "y^2=12*x^6+26*x^5+41*x^4+26*x^3+65*x^2+49*x+57", "y^2=7*x^6+24*x^4+26*x^2+58", "y^2=66*x^6+18*x^4+55*x^2+60", "y^2=59*x^6+24*x^5+11*x^4+66*x^3+65*x^2+70*x+70", "y^2=58*x^6+26*x^5+6*x^4+36*x^3+29*x^2+64*x+64", "y^2=9*x^6+9*x^5+20*x^4+68*x^3+7*x^2+54*x+13", "y^2=63*x^6+63*x^5+69*x^4+50*x^3+49*x^2+23*x+20", "y^2=54*x^6+41*x^5+29*x^4+31*x^3+70*x^2+25*x+21", "y^2=23*x^6+3*x^5+61*x^4+4*x^3+64*x^2+33*x+5", "y^2=57*x^6+32*x^5+52*x^4+3*x^3+52*x^2+32*x+57", "y^2=44*x^6+11*x^5+9*x^4+21*x^3+9*x^2+11*x+44", "y^2=36*x^6+43*x^5+13*x^4+7*x^3+61*x^2+12*x+54", "y^2=39*x^6+17*x^5+20*x^4+49*x^3+x^2+13*x+23", "y^2=31*x^6+36*x^4+39*x^2+54", "y^2=42*x^6+6*x^4+42*x^2+64", "y^2=52*x^6+63*x^5+54*x^4+23*x^3+54*x^2+63*x+52", "y^2=9*x^6+15*x^5+23*x^4+19*x^3+23*x^2+15*x+9", "y^2=67*x^6+7*x^5+42*x^4+64*x^3+23*x^2+32*x+54", "y^2=43*x^6+49*x^5+10*x^4+22*x^3+19*x^2+11*x+23", "y^2=58*x^6+14*x^4+27*x^2+14", "y^2=15*x^6+28*x^4+54*x^2+33", "y^2=58*x^6+44*x^5+30*x^4+42*x^3+59*x^2+50*x+49", "y^2=51*x^6+24*x^5+68*x^4+10*x^3+58*x^2+66*x+59", "y^2=27*x^6+35*x^5+12*x^4+52*x^3+54*x^2+24*x+42", "y^2=47*x^6+32*x^5+13*x^4+9*x^3+23*x^2+26*x+10", "y^2=38*x^6+52*x^5+64*x^4+37*x^3+44*x^2+47*x+12", "y^2=45*x^6+65*x^5+5*x^4+31*x^3+5*x^2+14*x+67", "y^2=31*x^6+29*x^5+35*x^4+4*x^3+35*x^2+27*x+43", "y^2=44*x^6+12*x^5+13*x^4+61*x^3+47*x^2+43*x+53", "y^2=24*x^6+13*x^5+20*x^4+x^3+45*x^2+17*x+16", "y^2=2*x^6+61*x^5+12*x^4+23*x^3+37*x^2+34*x+15", "y^2=14*x^6+x^5+13*x^4+19*x^3+46*x^2+25*x+34", "y^2=42*x^6+64*x^5+12*x^4+16*x^3+22*x+9", "y^2=10*x^6+22*x^5+13*x^4+41*x^3+12*x+63", "y^2=62*x^6+64*x^5+56*x^4+34*x^3+44*x^2+47*x+28", "y^2=8*x^6+22*x^5+37*x^4+25*x^3+24*x^2+45*x+54", "y^2=51*x^6+17*x^5+24*x^4+65*x^3+24*x^2+17*x+51", "y^2=2*x^6+48*x^5+26*x^4+29*x^3+26*x^2+48*x+2", "y^2=20*x^6+12*x^5+70*x^4+52*x^3+4*x^2+46*x+8", "y^2=69*x^6+13*x^5+64*x^4+9*x^3+28*x^2+38*x+56", "y^2=37*x^6+18*x^5+5*x^4+41*x^3+24*x^2+55*x+30", "y^2=20*x^6+55*x^5+41*x^4+5*x^3+50*x^2+66*x+31", "y^2=6*x^6+65*x^5+62*x^4+40*x^3+59*x^2+54*x+32", "y^2=18*x^6+16*x^5+39*x^4+7*x^3+23*x^2+44*x+70", "y^2=55*x^6+41*x^5+60*x^4+49*x^3+19*x^2+24*x+64", "y^2=23*x^6+4*x^5+55*x^4+24*x^3+67*x^2+3*x+62", "y^2=19*x^6+28*x^5+30*x^4+26*x^3+43*x^2+21*x+8", "y^2=53*x^6+14*x^5+61*x^4+12*x^3+46*x^2+25*x+56", "y^2=42*x^6+53*x^5+36*x^4+8*x^3+34*x^2+51*x+2", "y^2=52*x^6+7*x^5+2*x^4+38*x^3+39*x^2+65*x+17", "y^2=35*x^6+30*x^5+6*x^4+39*x^3+51*x^2+62*x+6", "y^2=32*x^6+68*x^5+42*x^4+60*x^3+2*x^2+8*x+42", "y^2=28*x^6+66*x^5+66*x^4+33*x^3+23*x^2+19*x+67", "y^2=59*x^6+62*x^5+49*x^4+65*x^3+62*x^2+29*x+42", "y^2=26*x^6+16*x^5+44*x^4+56*x^3+34*x^2+16*x", "y^2=22*x^6+63*x^5+31*x^4+2*x^3+27*x^2+23*x+42", "y^2=12*x^6+15*x^5+4*x^4+14*x^3+47*x^2+19*x+10", "y^2=37*x^6+25*x^5+52*x^4+52*x^3+36*x^2+41*x+68", "y^2=46*x^6+33*x^5+9*x^4+9*x^3+39*x^2+3*x+50", "y^2=24*x^6+60*x^5+62*x^4+12*x^3+43*x^2+21*x+70", "y^2=26*x^6+65*x^5+8*x^4+13*x^3+17*x^2+5*x+64", "y^2=16*x^6+50*x^5+70*x^4+49*x^3+6*x^2+54*x+36"], "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": 17, "g": 2, "galois_groups": ["2T1", "2T1"], "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": ["2.0.67.1"], "geometric_splitting_field": "2.0.67.1", "geometric_splitting_polynomials": [[17, -1, 1]], "group_structure_count": 5, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 77, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 77, "label": "2.71.a_ew", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["2.0.67.1", "2.0.67.1"], "p": 71, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, 126, 0, 5041], "poly_str": "1 0 126 0 5041 ", "primitive_models": [], "q": 71, "real_poly": [1, 0, -16], "simple_distinct": ["1.71.ae", "1.71.e"], "simple_factors": ["1.71.aeA", "1.71.eA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,-F-1"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.67.1", "splitting_polynomials": [[17, -1, 1]], "twist_count": 6, "twists": [["2.71.ai_gc", "2.5041.js_bmkk", 2], ["2.71.i_gc", "2.5041.js_bmkk", 2], ["2.71.a_aew", "2.25411681.ards_hcrqxi", 4], ["2.71.ae_acd", "2.128100283921.kusi_bhamwccqo", 6], ["2.71.e_acd", "2.128100283921.kusi_bhamwccqo", 6]], "weak_equivalence_count": 23, "zfv_index": 256, "zfv_index_factorization": [[2, 8]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 71824, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-F-1"]}