# Stored data for abelian variety isogeny class 2.19.ae_bg, downloaded from the LMFDB on 16 December 2025.
{"abvar_count": 314, "abvar_counts": [314, 148836, 47680586, 16979806224, 6136112715674, 2213253938430756, 798912229550492714, 288437738573765689344, 104127893249664448375226, 37590010803408969411493476], "abvar_counts_str": "314 148836 47680586 16979806224 6136112715674 2213253938430756 798912229550492714 288437738573765689344 104127893249664448375226 37590010803408969411493476 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.298277766668744, 0.542564572633739], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 16, "curve_counts": [16, 410, 6952, 130294, 2478136, 47044586, 893766064, 16983346654, 322689380368, 6131072349050], "curve_counts_str": "16 410 6952 130294 2478136 47044586 893766064 16983346654 322689380368 6131072349050 ", "curves": ["y^2=4*x^6+11*x^4+15*x^3+7*x^2+10*x+11", "y^2=4*x^6+14*x^5+9*x^4+8*x^3+18*x^2+15*x+8", "y^2=11*x^6+15*x^5+17*x^4+14*x^3+5*x^2+3*x+16", "y^2=6*x^6+5*x^4+10*x^3+18*x^2+2*x+2", "y^2=17*x^6+x^5+8*x^4+7*x^3+15*x^2+7*x+17", "y^2=18*x^6+8*x^5+x^4+16*x^3+15*x^2+18*x+12", "y^2=5*x^6+15*x^5+8*x^4+14*x^3+10*x^2+17*x+9", "y^2=3*x^6+11*x^5+15*x^4+17*x^3+x^2+12*x+15", "y^2=2*x^6+3*x^5+12*x^4+12*x^3+2*x^2+7*x+10", "y^2=5*x^6+17*x^5+9*x^4+4*x^3+12*x^2+11*x+1", "y^2=9*x^6+5*x^5+16*x^4+18*x^3+3*x^2+5*x", "y^2=13*x^6+17*x^5+13*x^4+x^3+9*x^2+5*x+1"], "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": 1, "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": ["4.0.5894400.1"], "geometric_splitting_field": "4.0.5894400.1", "geometric_splitting_polynomials": [[314, -20, 26, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 12, "is_cyclic": true, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 12, "label": "2.19.ae_bg", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.5894400.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -4, 32, -76, 361], "poly_str": "1 -4 32 -76 361 ", "primitive_models": [], "q": 19, "real_poly": [1, -4, -6], "simple_distinct": ["2.19.ae_bg"], "simple_factors": ["2.19.ae_bgA"], "simple_multiplicities": [1], "singular_primes": [], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.5894400.1", "splitting_polynomials": [[314, -20, 26, 0, 1]], "twist_count": 2, "twists": [["2.19.e_bg", "2.361.bw_bru", 2]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 3684, "zfv_singular_count": 0, "zfv_singular_primes": []}