# Stored data for abelian variety isogeny class 2.17.ab_bc, downloaded from the LMFDB on 20 September 2025.
{"abvar_count": 300, "abvar_counts": [300, 100800, 24292800, 6945120000, 2015933407500, 582500143411200, 168369852440244300, 48662783705128320000, 14063167243798844068800, 4064222215287001759320000], "abvar_counts_str": "300 100800 24292800 6945120000 2015933407500 582500143411200 168369852440244300 48662783705128320000 14063167243798844068800 4064222215287001759320000 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.381477984738588, 0.577979130377369], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 17, "curve_counts": [17, 345, 4946, 83153, 1419817, 24132510, 410319241, 6975985633, 118588574642, 2015989341225], "curve_counts_str": "17 345 4946 83153 1419817 24132510 410319241 6975985633 118588574642 2015989341225 ", "curves": ["y^2=5*x^6+2*x^5+5*x^4+15*x^3+6*x^2+15*x+3", "y^2=2*x^6+10*x^5+3*x^4+16*x^3+9*x^2+14*x+9", "y^2=5*x^6+2*x^5+13*x^4+2*x^3+14*x^2+5", "y^2=15*x^6+8*x^5+x^4+10*x^3+4*x^2+10*x", "y^2=5*x^6+4*x^5+6*x^4+2*x^3+3*x^2+11*x+10", "y^2=4*x^6+11*x^5+8*x^4+4*x^2+10*x+6", "y^2=6*x^6+4*x^5+9*x^4+16*x^3+2*x^2+x+2", "y^2=9*x^6+9*x^5+11*x^4+13*x^3+8*x^2+5*x+4", "y^2=5*x^6+16*x^5+7*x^4+5*x^3+16*x+4", "y^2=14*x^6+9*x^5+8*x^4+5*x^3+10*x+5", "y^2=9*x^6+12*x^5+4*x^4+16*x^3+6*x^2+14*x+6", "y^2=6*x^6+10*x^5+5*x^4+14*x^3+5*x^2+13*x+12", "y^2=15*x^5+10*x^4+15*x^3+9*x+7", "y^2=16*x^6+5*x^5+12*x^4+9*x^3+2*x^2+7*x+5", "y^2=7*x^6+2*x^5+14*x^4+14*x^3+9*x^2+6*x+9", "y^2=9*x^6+4*x^5+6*x^3+6*x^2+7*x", "y^2=4*x^6+16*x^5+5*x^2+2*x+16", "y^2=5*x^6+15*x^5+16*x^4+2*x^3+7*x^2+12*x+15", "y^2=9*x^6+15*x^5+4*x^4+10*x^3+6*x^2+13*x+14", "y^2=7*x^6+15*x^5+11*x^4+6*x^3+14*x^2+4*x+5", "y^2=6*x^6+8*x^5+15*x^4+14*x^3+16*x^2+15*x+5"], "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": 12, "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": ["2.0.59.1", "2.0.4.1"], "geometric_splitting_field": "4.0.55696.1", "geometric_splitting_polynomials": [[225, 0, -29, 0, 1]], "group_structure_count": 4, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 21, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 21, "label": "2.17.ab_bc", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.59.1", "2.0.4.1"], "p": 17, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 12], [1, 3, 2, 12], [2, 13, 1, 4]], "poly": [1, -1, 28, -17, 289], "poly_str": "1 -1 28 -17 289 ", "primitive_models": [], "principal_polarization_count": 33, "q": 17, "real_poly": [1, -1, -6], "simple_distinct": ["1.17.ad", "1.17.c"], "simple_factors": ["1.17.adA", "1.17.cA"], "simple_multiplicities": [1, 1], "singular_primes": ["5,3*V+7", "5,-4*F-3*V", "2,9*F+1"], "size": 138, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.55696.1", "splitting_polynomials": [[225, 0, -29, 0, 1]], "twist_count": 8, "twists": [["2.17.af_bo", "2.289.cd_bzc", 2], ["2.17.b_bc", "2.289.cd_bzc", 2], ["2.17.f_bo", "2.289.cd_bzc", 2], ["2.17.al_cg", "2.83521.aof_kjmu", 4], ["2.17.af_k", "2.83521.aof_kjmu", 4], ["2.17.f_k", "2.83521.aof_kjmu", 4], ["2.17.l_cg", "2.83521.aof_kjmu", 4]], "weak_equivalence_count": 12, "zfv_index": 100, "zfv_index_factorization": [[2, 2], [5, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 48, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 3776, "zfv_singular_count": 6, "zfv_singular_primes": ["5,3*V+7", "5,-4*F-3*V", "2,9*F+1"]}