# Stored data for abelian variety isogeny class 2.113.ay_kz, downloaded from the LMFDB on 07 October 2025.
{"abvar_count": 10319, "abvar_counts": [10319, 162947329, 2079874690544, 26576802076930201, 339448925230580404439, 4334521743815461045770496, 55347524650333995569477728679, 706732540733829712076859317914089, 9024267946700793045391318179955274096, 115230877640253992920680976725196439294449], "abvar_counts_str": "10319 162947329 2079874690544 26576802076930201 339448925230580404439 4334521743815461045770496 55347524650333995569477728679 706732540733829712076859317914089 9024267946700793045391318179955274096 115230877640253992920680976725196439294449 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.0197105444321555, 0.458251322724464], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 90, "curve_counts": [90, 12764, 1441458, 163000500, 18423927690, 2081951101118, 235260544576266, 26584441479705124, 3004041931836722514, 339456738971660776364], "curve_counts_str": "90 12764 1441458 163000500 18423927690 2081951101118 235260544576266 26584441479705124 3004041931836722514 339456738971660776364 ", "curves": ["y^2=99*x^6+38*x^5+65*x^4+95*x^3+12*x^2+77*x+75", "y^2=37*x^6+2*x^5+104*x^4+76*x^3+109*x^2+82*x+102", "y^2=108*x^6+27*x^5+110*x^4+14*x^3+100*x^2+23*x+4", "y^2=20*x^6+56*x^5+107*x^4+79*x^3+23*x^2+62*x+10", "y^2=49*x^6+5*x^5+67*x^4+35*x^3+71*x^2+107*x+107", "y^2=46*x^6+28*x^5+65*x^4+65*x^3+14*x^2+82*x+10", "y^2=80*x^6+109*x^5+94*x^4+50*x^3+81*x^2+53*x+58", "y^2=62*x^6+42*x^5+101*x^4+68*x^3+49*x^2+8*x+74", "y^2=61*x^6+107*x^5+14*x^4+27*x^3+12*x^2+22*x+54", "y^2=61*x^6+13*x^5+84*x^4+19*x^3+43*x^2+103*x+107", "y^2=97*x^6+40*x^5+70*x^4+99*x^3+36*x^2+40*x+98", "y^2=90*x^6+36*x^5+83*x^4+55*x^3+35*x^2+61*x+59", "y^2=88*x^6+42*x^5+x^4+69*x^3+90*x^2+44*x+25", "y^2=10*x^6+89*x^5+52*x^4+72*x^3+72*x^2+86*x+99", "y^2=90*x^6+97*x^5+51*x^4+22*x^3+8*x^2+42*x+23", "y^2=31*x^6+79*x^5+93*x^4+55*x^3+7*x^2+55*x+43", "y^2=43*x^6+80*x^5+80*x^4+6*x^3+96*x^2+106*x+58", "y^2=29*x^6+53*x^5+53*x^4+108*x^3+96*x^2+81*x+107", "y^2=41*x^6+10*x^5+109*x^4+32*x^3+48*x^2+43*x+112", "y^2=44*x^6+40*x^5+77*x^4+54*x^3+108*x^2+20*x+63"], "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": ["4.0.5556025.1"], "geometric_splitting_field": "4.0.5556025.1", "geometric_splitting_polynomials": [[236, 146, 27, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 20, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 20, "label": "2.113.ay_kz", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.5556025.1"], "p": 113, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 7, 1, 10], [1, 7, 2, 10]], "poly": [1, -24, 285, -2712, 12769], "poly_str": "1 -24 285 -2712 12769 ", "primitive_models": [], "principal_polarization_count": 20, "q": 113, "real_poly": [1, -24, 59], "simple_distinct": ["2.113.ay_kz"], "simple_factors": ["2.113.ay_kzA"], "simple_multiplicities": [1], "singular_primes": ["2,-F^2+3*F+1"], "size": 40, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.5556025.1", "splitting_polynomials": [[236, 146, 27, -1, 1]], "twist_count": 2, "twists": [["2.113.y_kz", "2.12769.ag_abiqn", 2]], "weak_equivalence_count": 2, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 20, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 769, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-F^2+3*F+1"]}