# Stored data for abelian variety isogeny class 2.41.a_abn, downloaded from the LMFDB on 21 September 2025.
{"abvar_count": 1643, "abvar_counts": [1643, 2699449, 4750241600, 7995338725609, 13422659167481003, 22564795258370560000, 37929227194790075968283, 63759067042324612439597769, 107178930967532418525525550400, 180167779126361812543840365886009], "abvar_counts_str": "1643 2699449 4750241600 7995338725609 13422659167481003 22564795258370560000 37929227194790075968283 63759067042324612439597769 107178930967532418525525550400 180167779126361812543840365886009 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.171113726077932, 0.828886273922068], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 42, "curve_counts": [42, 1604, 68922, 2829444, 115856202, 4750378958, 194754273882, 7984929753604, 327381934393962, 13422659024809604], "curve_counts_str": "42 1604 68922 2829444 115856202 4750378958 194754273882 7984929753604 327381934393962 13422659024809604 ", "curves": ["y^2=40*x^6+9*x^5+30*x^4+12*x^3+6*x^2+6*x+29", "y^2=35*x^6+13*x^5+16*x^4+31*x^3+36*x^2+36*x+10", "y^2=8*x^6+14*x^5+12*x^4+21*x^3+30*x^2+4*x+31", "y^2=14*x^6+15*x^5+30*x^3+13*x^2+12*x+32", "y^2=27*x^6+4*x^5+34*x^4+25*x^3+38*x^2+21*x+4", "y^2=39*x^6+24*x^5+40*x^4+27*x^3+23*x^2+3*x+24", "y^2=x^6+12*x^5+29*x^4+3*x^3+4*x^2+21*x+8", "y^2=29*x^6+15*x^5+4*x^4+14*x^3+27*x^2+26*x+11", "y^2=10*x^6+8*x^5+24*x^4+2*x^3+39*x^2+33*x+25", "y^2=35*x^6+21*x^5+28*x^4+22*x^3+11*x^2+13*x+39", "y^2=39*x^6+24*x^4+30*x^3+24*x^2+39", "y^2=29*x^6+21*x^4+16*x^3+21*x^2+29", "y^2=19*x^6+13*x^5+25*x^4+x^3+13*x^2+20*x+30", "y^2=32*x^6+37*x^5+27*x^4+6*x^3+37*x^2+38*x+16", "y^2=17*x^6+28*x^5+40*x^4+7*x^3+37*x^2+13*x+12", "y^2=28*x^6+20*x^5+18*x^4+11*x^3+27*x^2+10*x+20", "y^2=4*x^6+38*x^5+26*x^4+25*x^3+39*x^2+19*x+38"], "dim1_distinct": 2, "dim1_factors": 2, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 8, "g": 2, "galois_groups": ["2T1", "2T1"], "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": ["2.0.43.1"], "geometric_splitting_field": "2.0.43.1", "geometric_splitting_polynomials": [[11, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 17, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 17, "label": "2.41.a_abn", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.43.1", "2.0.43.1"], "p": 41, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, -39, 0, 1681], "poly_str": "1 0 -39 0 1681 ", "primitive_models": [], "q": 41, "real_poly": [1, 0, -121], "simple_distinct": ["1.41.al", "1.41.l"], "simple_factors": ["1.41.alA", "1.41.lA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,9*F+V+9", "11,16*F+80", "11,-6*F-V+14"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.43.1", "splitting_polynomials": [[11, -1, 1]], "twist_count": 6, "twists": [["2.41.aw_hv", "2.1681.ada_hfv", 2], ["2.41.w_hv", "2.1681.ada_hfv", 2], ["2.41.a_bn", "2.2825761.flq_tujzf", 4], ["2.41.al_dc", "2.4750104241.pqka_dnvokpvy", 6], ["2.41.l_dc", "2.4750104241.pqka_dnvokpvy", 6]], "weak_equivalence_count": 8, "zfv_index": 484, "zfv_index_factorization": [[2, 2], [11, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 1849, "zfv_singular_count": 6, "zfv_singular_primes": ["2,9*F+V+9", "11,16*F+80", "11,-6*F-V+14"]}