# Stored data for abelian variety isogeny class 4.5.a_i_a_co, downloaded from the LMFDB on 02 November 2025.
{"abvar_count": 900, "abvar_counts": [900, 810000, 236852100, 189747360000, 95475372322500, 56098917274410000, 37252410859779596100, 23305722394375618560000, 14551899345840973108176900, 9115546720119999044006250000], "abvar_counts_str": "900 810000 236852100 189747360000 95475372322500 56098917274410000 37252410859779596100 23305722394375618560000 14551899345840973108176900 9115546720119999044006250000 ", "angle_corank": 3, "angle_rank": 1, "angles": [0.315494940217227, 0.315494940217227, 0.684505059782773, 0.684505059782773], "center_dim": 4, "curve_count": 6, "curve_counts": [6, 42, 126, 762, 3126, 14682, 78126, 391002, 1953126, 9787722], "curve_counts_str": "6 42 126 762 3126 14682 78126 391002 1953126 9787722 ", "curves": ["y^2=x^10+2*x^6+x^4+3", "y^2=x^10+x^8+2*x^7+4*x^6+x^5+x^4+2", "y^2=2*x^10+2*x^8+4*x^7+3*x^6+2*x^5+2*x^4+4", "y^2=x^10+3*x^9+4*x^8+2*x^6+x^4+3*x^2+2*x+3", "y^2=x^10+3*x^6+2*x^4+4", "y^2=2*x^10+x^6+4*x^4+3", "y^2=x^9+x^7+2*x^6+2*x^5+4*x^3+3*x^2+4", "y^2=2*x^9+2*x^7+4*x^6+4*x^5+3*x^3+x^2+3"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 1, "dim2_factors": 2, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "g": 4, "galois_groups": ["4T2"], "geom_dim1_distinct": 1, "geom_dim1_factors": 4, "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": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.84.1"], "geometric_splitting_field": "2.0.84.1", "geometric_splitting_polynomials": [[21, 0, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 8, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": false, "label": "4.5.a_i_a_co", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 24, "newton_coelevation": 6, "newton_elevation": 0, "number_fields": ["4.0.112896.2"], "p": 5, "p_rank": 4, "p_rank_deficit": 0, "poly": [1, 0, 8, 0, 66, 0, 200, 0, 625], "poly_str": "1 0 8 0 66 0 200 0 625 ", "primitive_models": [], "q": 5, "real_poly": [1, 0, -12, 0, 36], "simple_distinct": ["2.5.a_e"], "simple_factors": ["2.5.a_eA", "2.5.a_eB"], "simple_multiplicities": [2], "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "4.0.112896.2", "splitting_polynomials": [[25, 0, 4, 0, 1]], "twist_count": 8, "twists": [["4.5.a_ae_a_aj", "4.125.a_ase_a_eyqc", 3], ["4.5.a_ai_a_co", "4.625.fg_nyy_xlum_bbarji", 4], ["4.5.a_a_a_bi", "4.625.fg_nyy_xlum_bbarji", 4], ["4.5.a_a_a_abi", "4.390625.om_dnxvg_bljmsvo_epeagubva", 8], ["4.5.a_e_a_aj", "4.244140625.afoqy_otzmcmm_axyuoluppca_zvtotmlyllres", 12], ["4.5.ag_s_abk_ct", "4.59604644775390625.abkuyrlg_dgmxqdbzmqvyy_acvozkbasqqoeourpswm_dhrnqwzkjaxzhvlztiqfhsgpi", 24], ["4.5.g_s_bk_ct", "4.59604644775390625.abkuyrlg_dgmxqdbzmqvyy_acvozkbasqqoeourpswm_dhrnqwzkjaxzhvlztiqfhsgpi", 24]]}