# Stored data for abelian variety isogeny class 2.41.ah_i, downloaded from the LMFDB on 07 October 2026.
{"abvar_count": 1396, "abvar_counts": [1396, 2769664, 4679107216, 7978504612864, 13422042056685076, 22562250720688537600, 37929091847410326707476, 63759027042012462991847424, 107178910088031659300048772496, 180167780227118177677992753289984], "abvar_counts_str": "1396 2769664 4679107216 7978504612864 13422042056685076 22562250720688537600 37929091847410326707476 63759027042012462991847424 107178910088031659300048772496 180167780227118177677992753289984 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.0174146042242129, 0.649252062442454], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 35, "curve_counts": [35, 1649, 67886, 2823489, 115850875, 4749843278, 194753578915, 7984924744129, 327381870616766, 13422659106816929], "curve_counts_str": "35 1649 67886 2823489 115850875 4749843278 194753578915 7984924744129 327381870616766 13422659106816929 ", "curves": ["y^2=25*x^6+23*x^5+19*x^4+9*x^3+14*x^2+31*x+22", "y^2=18*x^6+39*x^5+31*x^4+17*x^3+6*x^2+39*x+31", "y^2=23*x^6+7*x^5+35*x^4+36*x^3+5*x^2+25*x+4", "y^2=2*x^6+9*x^5+12*x^4+28*x^3+35*x^2+37*x+9", "y^2=x^6+29*x^5+39*x^4+30*x^3+14*x^2+38*x+24", "y^2=19*x^6+4*x^5+3*x^4+35*x^3+2*x^2+17*x+11", "y^2=22*x^6+34*x^5+31*x^4+14*x^3+38*x^2+39*x+1", "y^2=34*x^5+37*x^4+16*x^3+30*x^2+8*x+5", "y^2=8*x^6+x^5+18*x^4+3*x^2+2*x+6", "y^2=35*x^6+17*x^5+29*x^4+16*x^3+2*x^2+15*x+12"], "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": 4, "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": 3, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.115.1"], "geometric_splitting_field": "2.0.115.1", "geometric_splitting_polynomials": [[29, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 10, "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": 10, "label": "2.41.ah_i", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.119025.3"], "p": 41, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 2], [1, 7, 1, 4]], "poly": [1, -7, 8, -287, 1681], "poly_str": "1 -7 8 -287 1681 ", "primitive_models": [], "principal_polarization_count": 10, "q": 41, "real_poly": [1, -7, -74], "simple_distinct": ["2.41.ah_i"], "simple_factors": ["2.41.ah_iA"], "simple_multiplicities": [1], "singular_primes": ["2,-F^2-F+4"], "size": 16, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.119025.3", "splitting_polynomials": [[841, -29, -28, -1, 1]], "twist_count": 6, "twists": [["2.41.h_i", "2.1681.abh_awu", 2], ["2.41.o_fb", "2.68921.abnw_xcvu", 3], ["2.41.ao_fb", "2.4750104241.aowbc_dhwohndm", 6], ["2.41.a_bh", "2.4750104241.aowbc_dhwohndm", 6], ["2.41.a_abh", "2.22563490300366186081.abwstkkxg_bpaiiduwrdndjfy", 12]], "weak_equivalence_count": 4, "zfv_index": 8, "zfv_index_factorization": [[2, 3]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 8, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 64, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-F^2-F+4"]}