# Stored data for abelian variety isogeny class 4.3.a_ab_a_i, downloaded from the LMFDB on 22 September 2025.
{"abvar_count": 80, "abvar_counts": [80, 6400, 527360, 64000000, 3512856400, 278108569600, 22858581253840, 1964262400000000, 150085819531627520, 12340160087020960000], "abvar_counts_str": "80 6400 527360 64000000 3512856400 278108569600 22858581253840 1964262400000000 150085819531627520 12340160087020960000 ", "angle_corank": 2, "angle_rank": 2, "angles": [0.144188681099749, 0.32433441433903, 0.67566558566097, 0.855811318900252], "center_dim": 8, "cohen_macaulay_max": 3, "curve_count": 4, "curve_counts": [4, 8, 28, 112, 244, 722, 2188, 6944, 19684, 59928], "curve_counts_str": "4 8 28 112 244 722 2188 6944 19684 59928 ", "curves": ["y^2=x^9+2*x^7+2*x^5+2*x^3+2*x", "y^2=x^10+x^9+2*x^8+2*x^6+x^4+x^2+x+2", "y^2=x^10+x^9+2*x^8+x^6+x^4+2*x^2+x", "y^2=x^9+x^7+2*x^5+x^3+2*x", "y^2=x^9+x^8+x^5+2*x^3+2*x^2+2*x", "x*y+t^2=y^2*z+y*z^2-z^3+x^2*t+x*z*t+y*z*t+z^2*t=0", "x*y+t^2=y^2*z-y*z^2+z^3+x^2*t+x*z*t-z^2*t=0", "x*y+t^2=y^3+x*z^2-y*z^2+z^3+x^2*t+y^2*t+y*z*t+z^2*t=0", "x*y+t^2=y^2*z+x*z^2+y*z^2+z^3+x^2*t-x*y*t+x*z*t+y*z*t+z^2*t=0", "x*y+t^2=y^3+x*y*z+y^2*z+x*z^2-y*z^2-z^3+x^2*t-y^2*t-x*z*t+y*z*t+z^2*t=0", "x*y+t^2=x^2*z-x*y*z+y^2*z+y*z^2-z^3+y^2*t+y*z*t=0", "x^2+y^2+z*t=y^2*z+y*z^2+y*z*t+z^2*t+x*t^2-y*t^2=0", "x^2+y^2+z*t=y^3-y*z^2-z^3+y^2*t+x*z*t+z^2*t-y*t^2-z*t^2=0", "x^2+y^2+z*t=y^3-y*z^2-z^3+y^2*t+x*z*t+y*z*t+z^2*t-x*t^2=0", "x^2+y^2+z*t=y^3+y^2*z+y*z^2+x*z*t+z^2*t-x*t^2-z*t^2+t^3=0"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 1, "dim4_factors": 1, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 24, "g": 4, "galois_groups": ["8T18"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 2, "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": 2, "geometric_galois_groups": ["4T3"], "geometric_number_fields": ["4.0.67240.1"], "geometric_splitting_field": "4.0.65600.5", "geometric_splitting_polynomials": [[25, -10, 1, -2, 1]], "group_structure_count": 5, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 5, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 15, "label": "4.3.a_ab_a_i", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 6, "newton_elevation": 0, "number_fields": ["8.0.4521217600.1"], "p": 3, "p_rank": 4, "p_rank_deficit": 0, "poly": [1, 0, -1, 0, 8, 0, -9, 0, 81], "poly_str": "1 0 -1 0 8 0 -9 0 81 ", "primitive_models": [], "q": 3, "real_poly": [1, 0, -13, 0, 32], "simple_distinct": ["4.3.a_ab_a_i"], "simple_factors": ["4.3.a_ab_a_iA"], "simple_multiplicities": [1], "singular_primes": ["2,10*F^3+16*F+11*V^3-3*V^2+23*V+2", "2,-6*F^3-2*F^2+9*F-2*V^2-26*V-1"], "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "8.0.4521217600.1", "splitting_polynomials": [[16, 0, 4, 0, -2, 0, 1, 0, 1], [20, -30, 41, 15, -13, 6, 3, -3, 1]], "twist_count": 2, "twists": [["4.3.a_b_a_i", "4.81.be_yr_mvm_fhiq", 4]], "weak_equivalence_count": 30, "zfv_index": 256, "zfv_index_factorization": [[2, 8]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 8, "zfv_plus_index_factorization": [[2, 3]], "zfv_plus_norm": 400, "zfv_singular_count": 4, "zfv_singular_primes": ["2,10*F^3+16*F+11*V^3-3*V^2+23*V+2", "2,-6*F^3-2*F^2+9*F-2*V^2-26*V-1"]}