# Stored data for abelian variety isogeny class 2.41.a_ay, downloaded from the LMFDB on 13 October 2025.
{"abvar_count": 1658, "abvar_counts": [1658, 2748964, 4750211450, 8000683788304, 13422659079289178, 22564508819711102500, 37929227195255799558938, 63758997213913271532847104, 107178930967531488809899605050, 180167776758824203655377747915684], "abvar_counts_str": "1658 2748964 4750211450 8000683788304 13422659079289178 22564508819711102500 37929227195255799558938 63758997213913271532847104 107178930967531488809899605050 180167776758824203655377747915684 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.20272597943457, 0.797274020565431], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 42, "curve_counts": [42, 1634, 68922, 2831334, 115856202, 4750318658, 194754273882, 7984921008574, 327381934393962, 13422658848425954], "curve_counts_str": "42 1634 68922 2831334 115856202 4750318658 194754273882 7984921008574 327381934393962 13422658848425954 ", "curves": ["y^2=34*x^6+9*x^5+20*x^4+36*x^3+22*x^2+5*x+15", "y^2=40*x^6+13*x^5+38*x^4+11*x^3+9*x^2+30*x+8", "y^2=14*x^6+22*x^5+36*x^4+31*x^3+26*x^2+28*x+25", "y^2=2*x^6+9*x^5+11*x^4+22*x^3+33*x^2+4*x+27", "y^2=37*x^6+11*x^5+35*x^4+36*x^3+4*x^2+4*x+23", "y^2=17*x^6+25*x^5+5*x^4+11*x^3+24*x^2+24*x+15", "y^2=26*x^6+13*x^5+39*x^4+8*x^3+14*x^2+16*x+18", "y^2=33*x^6+37*x^5+29*x^4+7*x^3+2*x^2+14*x+26"], "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": ["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": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.6148.1"], "geometric_splitting_field": "2.0.6148.1", "geometric_splitting_polynomials": [[1537, 0, 1]], "group_structure_count": 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": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 8, "label": "2.41.a_ay", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.604766464.2"], "p": 41, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 4], [1, 47, 1, 16]], "poly": [1, 0, -24, 0, 1681], "poly_str": "1 0 -24 0 1681 ", "primitive_models": [], "principal_polarization_count": 16, "q": 41, "real_poly": [1, 0, -106], "simple_distinct": ["2.41.a_ay"], "simple_factors": ["2.41.a_ayA"], "simple_multiplicities": [1], "singular_primes": [], "size": 32, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.604766464.2", "splitting_polynomials": [[1681, 0, -24, 0, 1]], "twist_count": 2, "twists": [["2.41.a_y", "2.2825761.igi_bdjeew", 4]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_pic_size": 32, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 3364, "zfv_singular_count": 0, "zfv_singular_primes": []}