# Stored data for abelian variety isogeny class 2.23.ak_by, downloaded from the LMFDB on 01 May 2026.
{"abvar_count": 340, "abvar_counts": [340, 278800, 145742020, 77729440000, 41387589633700, 21914624175437200, 11592576505220420980, 6132528020114864640000, 3244144595618519448758260, 1716155831334532959208570000], "abvar_counts_str": "340 278800 145742020 77729440000 41387589633700 21914624175437200 11592576505220420980 6132528020114864640000 3244144595618519448758260 1716155831334532959208570000 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.0138570610432113, 0.486142938956789], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 14, "curve_counts": [14, 530, 11978, 277758, 6430294, 148035890, 3404749138, 78309933118, 1801149155774, 41426511213650], "curve_counts_str": "14 530 11978 277758 6430294 148035890 3404749138 78309933118 1801149155774 41426511213650 ", "curves": ["y^2=18*x^6+16*x^5+4*x^4+19*x^2+2*x+20", "y^2=20*x^6+4*x^5+19*x+20", "y^2=10*x^6+3*x^5+4*x^4+4*x^2+20*x+10", "y^2=20*x^6+6*x^5+19*x^4+18*x^3+14*x^2+22*x+15"], "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": 3, "g": 2, "galois_groups": ["4T2"], "geom_dim1_distinct": 1, "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": 2, "geometric_extension_degree": 4, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.84.1"], "geometric_splitting_field": "2.0.84.1", "geometric_splitting_polynomials": [[21, 0, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 4, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 4, "label": "2.23.ak_by", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 8, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.7056.1"], "p": 23, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -10, 50, -230, 529], "poly_str": "1 -10 50 -230 529 ", "primitive_models": [], "q": 23, "real_poly": [1, -10, 4], "simple_distinct": ["2.23.ak_by"], "simple_factors": ["2.23.ak_byA"], "simple_multiplicities": [1], "singular_primes": ["2,F^2-F-4"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.7056.1", "splitting_polynomials": [[25, 0, 11, 0, 1]], "twist_count": 4, "twists": [["2.23.k_by", "2.529.a_aboc", 2], ["2.23.k_by", "2.279841.adce_dpqck", 4], ["2.23.a_ae", "2.78310985281.achwlw_cbyxyeuqw", 8], ["2.23.a_e", "2.78310985281.achwlw_cbyxyeuqw", 8]], "weak_equivalence_count": 3, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 16, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F^2-F-4"]}