# Stored data for abelian variety isogeny class 2.41.as_gg, downloaded from the LMFDB on 07 November 2025.
{"abvar_count": 1088, "abvar_counts": [1088, 2828800, 4798733888, 8002109440000, 13425660552953408, 22563490302651251200, 37929053455415256638528, 63758973775802534461440000, 107178921857613238311108542528, 180167782956420913420611757120000], "abvar_counts_str": "1088 2828800 4798733888 8002109440000 13425660552953408 22563490302651251200 37929053455415256638528 63758973775802534461440000 107178921857613238311108542528 180167782956420913420611757120000 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.214776712522723, 0.285223287477277], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 24, "curve_counts": [24, 1682, 69624, 2831838, 115882104, 4750104242, 194753381784, 7984918073278, 327381906567384, 13422659310152402], "curve_counts_str": "24 1682 69624 2831838 115882104 4750104242 194753381784 7984918073278 327381906567384 13422659310152402 ", "curves": ["y^2=18*x^6+39*x^5+13*x^4+5*x^3+3*x^2+21*x+10", "y^2=22*x^6+7*x^5+18*x^4+27*x^3+31*x^2+30*x+14", "y^2=19*x^6+27*x^5+13*x^4+25*x^3+28*x^2+27*x+22", "y^2=28*x^6+40*x^5+21*x^4+9*x^3+18*x^2+16*x+26", "y^2=26*x^6+3*x^5+22*x^4+25*x^3+17*x^2+30*x+22", "y^2=28*x^6+23*x^5+16*x^4+26*x^3+2*x^2+x+26", "y^2=27*x^6+11*x^5+24*x^4+31*x^3+19*x^2+38*x+17", "y^2=31*x^6+27*x^4+31*x^3+19*x^2+1", "y^2=17*x^6+11*x^4+32*x^3+24*x^2+30", "y^2=4*x^6+17*x^4+5*x^3+24*x^2+37"], "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": 14, "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": 4, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.4.1"], "geometric_splitting_field": "2.0.4.1", "geometric_splitting_polynomials": [[1, 0, 1]], "group_structure_count": 6, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 10, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 10, "label": "2.41.as_gg", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.4.1", "2.0.4.1"], "p": 41, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -18, 162, -738, 1681], "poly_str": "1 -18 162 -738 1681 ", "primitive_models": [], "q": 41, "real_poly": [1, -18, 80], "simple_distinct": ["1.41.ak", "1.41.ai"], "simple_factors": ["1.41.akA", "1.41.aiA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,5*V-55", "5,9*F^2-90*F+361"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.4.1", "splitting_polynomials": [[1, 0, 1]], "twist_count": 16, "twists": [["2.41.ac_c", "2.1681.a_emw", 2], ["2.41.c_c", "2.1681.a_emw", 2], ["2.41.s_gg", "2.1681.a_emw", 2], ["2.41.au_ha", "2.2825761.izs_bgorgw", 4], ["2.41.aq_fq", "2.2825761.izs_bgorgw", 4], ["2.41.a_as", "2.2825761.izs_bgorgw", 4], ["2.41.a_s", "2.2825761.izs_bgorgw", 4], ["2.41.q_fq", "2.2825761.izs_bgorgw", 4], ["2.41.u_ha", "2.2825761.izs_bgorgw", 4], ["2.41.a_adc", "2.7984925229121.aprdou_fhueqoesyo", 8], ["2.41.a_dc", "2.7984925229121.aprdou_fhueqoesyo", 8], ["2.41.ak_ch", "2.22563490300366186081.ouqvbrw_uhpqxurdifkmyg", 12], ["2.41.ai_x", "2.22563490300366186081.ouqvbrw_uhpqxurdifkmyg", 12], ["2.41.i_x", "2.22563490300366186081.ouqvbrw_uhpqxurdifkmyg", 12], ["2.41.k_ch", "2.22563490300366186081.ouqvbrw_uhpqxurdifkmyg", 12]], "weak_equivalence_count": 18, "zfv_index": 80, "zfv_index_factorization": [[2, 4], [5, 1]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 6400, "zfv_singular_count": 4, "zfv_singular_primes": ["2,5*V-55", "5,9*F^2-90*F+361"]}