# Stored data for abelian variety isogeny class 2.41.a_ap, downloaded from the LMFDB on 15 October 2025.
{"abvar_count": 1667, "abvar_counts": [1667, 2778889, 4750176512, 8002669552201, 13422659125827827, 22564176895156486144, 37929227195289567246467, 63758964013038451340015625, 107178930967531131949058861312, 180167778008169044896628047541929], "abvar_counts_str": "1667 2778889 4750176512 8002669552201 13422659125827827 22564176895156486144 37929227195289567246467 63758964013038451340015625 107178930967531131949058861312 180167778008169044896628047541929 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.220721427874418, 0.779278572125582], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 42, "curve_counts": [42, 1652, 68922, 2832036, 115856202, 4750248782, 194754273882, 7984916850628, 327381934393962, 13422658941503252], "curve_counts_str": "42 1652 68922 2832036 115856202 4750248782 194754273882 7984916850628 327381934393962 13422658941503252 ", "curves": ["y^2=7*x^6+29*x^5+6*x^4+36*x^3+17*x^2+25*x+34", "y^2=x^6+10*x^5+36*x^4+11*x^3+20*x^2+27*x+40", "y^2=19*x^6+25*x^5+31*x^4+26*x^3+20*x^2+20*x+31", "y^2=33*x^6+5*x^5+16*x^4+x^3+4*x^2+40*x+16", "y^2=3*x^6+8*x^5+22*x^4+30*x^3+32*x^2+30*x+21", "y^2=18*x^6+7*x^5+9*x^4+16*x^3+28*x^2+16*x+3", "y^2=5*x^6+3*x^5+14*x^4+30*x^3+4*x^2+36*x+21", "y^2=4*x^6+17*x^5+17*x^4+x^3+4*x^2+5*x+38", "y^2=24*x^6+20*x^5+20*x^4+6*x^3+24*x^2+30*x+23", "y^2=25*x^6+38*x^5+36*x^4+31*x^3+x^2+10*x+30", "y^2=23*x^6+10*x^5+36*x^4+16*x^3+12*x^2+23*x+24", "y^2=15*x^6+19*x^5+11*x^4+14*x^3+31*x^2+15*x+21", "y^2=26*x^6+30*x^5+20*x^4+35*x^3+23*x^2+23*x+40", "y^2=2*x^6+x^5+35*x^4+19*x^2+14*x+19", "y^2=12*x^6+6*x^5+5*x^4+32*x^2+2*x+32", "y^2=31*x^6+17*x^5+9*x^4+9*x^3+x^2+15*x+28", "y^2=22*x^6+20*x^5+13*x^4+13*x^3+6*x^2+8*x+4", "y^2=19*x^6+10*x^5+39*x^4+12*x^3+31*x^2+32*x+13", "y^2=32*x^6+19*x^5+29*x^4+31*x^3+22*x^2+28*x+37", "y^2=x^6+6*x^5+38*x^4+40*x^3+39*x^2+10*x+1", "y^2=29*x^6+35*x^5+28*x^4+4*x^3+30*x^2+28*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": 2, "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": ["2.0.6499.1"], "geometric_splitting_field": "2.0.6499.1", "geometric_splitting_polynomials": [[1625, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 21, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 21, "label": "2.41.a_ap", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.42237001.1"], "p": 41, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 5, 1, 7], [1, 47, 1, 21]], "poly": [1, 0, -15, 0, 1681], "poly_str": "1 0 -15 0 1681 ", "primitive_models": [], "principal_polarization_count": 28, "q": 41, "real_poly": [1, 0, -97], "simple_distinct": ["2.41.a_ap"], "simple_factors": ["2.41.a_apA"], "simple_multiplicities": [1], "singular_primes": ["2,F^2+4*F-5*V-4"], "size": 28, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.42237001.1", "splitting_polynomials": [[1681, 0, -15, 0, 1]], "twist_count": 2, "twists": [["2.41.a_p", "2.2825761.jhi_bhxlpj", 4]], "weak_equivalence_count": 2, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 21, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 4489, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F^2+4*F-5*V-4"]}