# Stored data for abelian variety isogeny class 2.71.x_kk, downloaded from the LMFDB on 01 May 2026.
{"abvar_count": 6968, "abvar_counts": [6968, 25475008, 127541686688, 646150242812672, 3255116198266241608, 16409670977338814835712, 82721243150852792036785832, 416997609757941213215243414528, 2102085018959487027822915048612512, 10596610575755787493260223916677056448], "abvar_counts_str": "6968 25475008 127541686688 646150242812672 3255116198266241608 16409670977338814835712 82721243150852792036785832 416997609757941213215243414528 2102085018959487027822915048612512 10596610575755787493260223916677056448 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.689225310369823, 0.797689990552892], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 95, "curve_counts": [95, 5053, 356348, 25427289, 1804158765, 128100192094, 9095123726819, 645753510559185, 45848500736549204, 3255243550814616693], "curve_counts_str": "95 5053 356348 25427289 1804158765 128100192094 9095123726819 645753510559185 45848500736549204 3255243550814616693 ", "curves": ["y^2=22*x^6+64*x^5+42*x^4+54*x^3+35*x^2+36*x+65", "y^2=4*x^6+5*x^5+38*x^4+26*x^3+34*x^2+30*x+50", "y^2=62*x^6+58*x^5+51*x^4+62*x^3+49*x^2+30*x+4", "y^2=18*x^6+29*x^5+7*x^4+43*x^3+40*x^2+64*x+50", "y^2=69*x^6+21*x^5+22*x^4+64*x^3+25*x^2+8*x+58", "y^2=60*x^6+51*x^5+19*x^4+25*x^3+33*x^2+50*x+50", "y^2=14*x^6+16*x^5+43*x^4+37*x^3+54*x^2+32", "y^2=40*x^6+50*x^5+45*x^4+16*x^3+27*x^2+47*x+28", "y^2=19*x^6+3*x^5+50*x^4+40*x^3+17*x^2+60*x", "y^2=56*x^6+44*x^5+26*x^4+3*x^3+68*x^2+23*x+1", "y^2=18*x^6+43*x^5+57*x^4+13*x^3+35*x^2+61*x+15", "y^2=53*x^6+70*x^5+22*x^4+2*x^3+59*x^2+2*x+13", "y^2=30*x^6+6*x^5+12*x^4+x^3+15*x^2+13*x+24", "y^2=45*x^6+6*x^5+14*x^4+28*x^3+16*x^2+69*x+45", "y^2=25*x^6+70*x^5+59*x^4+6*x^3+25*x^2+62*x+22", "y^2=54*x^6+63*x^5+16*x^4+20*x^3+13*x^2+41*x+43", "y^2=43*x^6+23*x^5+8*x^4+29*x^3+35*x^2+16*x+25", "y^2=10*x^6+40*x^5+36*x^4+18*x^3+16*x^2+42*x+39", "y^2=60*x^6+20*x^5+43*x^4+40*x^3+15*x^2+34*x", "y^2=9*x^6+35*x^5+37*x^4+39*x^3+27*x^2+12*x+59", "y^2=6*x^6+13*x^5+39*x^4+11*x^3+34*x^2+20*x+40", "y^2=58*x^6+65*x^5+8*x^4+32*x^3+63*x^2+3*x+14", "y^2=22*x^6+29*x^5+63*x^4+3*x^3+32*x^2+63*x+44", "y^2=14*x^6+48*x^5+16*x^4+52*x^3+52*x^2+37*x+5", "y^2=21*x^6+53*x^5+41*x^4+11*x^3+51*x^2+15*x+22", "y^2=43*x^6+33*x^5+62*x^4+42*x^3+3*x^2+13*x+33", "y^2=31*x^6+63*x^5+63*x^4+26*x^3+16*x^2+54*x+11", "y^2=32*x^6+23*x^5+47*x^4+31*x^3+39*x^2+69*x+27", "y^2=52*x^6+36*x^5+52*x^4+66*x^3+59*x^2+52*x", "y^2=45*x^6+22*x^5+5*x^4+23*x^3+50*x^2+51*x+68"], "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": ["4T3"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 1, "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": ["4T3"], "geometric_number_fields": ["4.0.1409453.1"], "geometric_splitting_field": "4.0.1409453.1", "geometric_splitting_polynomials": [[1294, -11, 69, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 30, "is_cyclic": false, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 30, "label": "2.71.x_kk", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.1409453.1"], "p": 71, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 23, 270, 1633, 5041], "poly_str": "1 23 270 1633 5041 ", "primitive_models": [], "q": 71, "real_poly": [1, 23, 128], "simple_distinct": ["2.71.x_kk"], "simple_factors": ["2.71.x_kkA"], "simple_multiplicities": [1], "singular_primes": ["2,10*F+3*V+69"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.1409453.1", "splitting_polynomials": [[1294, -11, 69, -1, 1]], "twist_count": 2, "twists": [["2.71.ax_kk", "2.5041.l_lqm", 2]], "weak_equivalence_count": 2, "zfv_index": 2, "zfv_index_factorization": [[2, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 19508, "zfv_singular_count": 2, "zfv_singular_primes": ["2,10*F+3*V+69"]}