# Stored data for abelian variety isogeny class 2.83.a_aco, downloaded from the LMFDB on 01 May 2026.
{"abvar_count": 6824, "abvar_counts": [6824, 46566976, 326941449896, 2253186720449536, 15516041180195074664, 106890711660098678410816, 736365263311651451502847976, 5072820326623539632520898560000, 34946659039493167582538799876753704, 240747533905509365439635381164534712896], "abvar_counts_str": "6824 46566976 326941449896 2253186720449536 15516041180195074664 106890711660098678410816 736365263311651451502847976 5072820326623539632520898560000 34946659039493167582538799876753704 240747533905509365439635381164534712896 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.184923259698002, 0.815076740301998], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 84, "curve_counts": [84, 6758, 571788, 47477166, 3939040644, 326942526422, 27136050989628, 2252292244424158, 186940255267540404, 15516041173184295878], "curve_counts_str": "84 6758 571788 47477166 3939040644 326942526422 27136050989628 2252292244424158 186940255267540404 15516041173184295878 ", "curves": ["y^2=43*x^6+30*x^5+10*x^4+34*x^3+56*x^2+79*x+29", "y^2=3*x^6+60*x^5+20*x^4+68*x^3+29*x^2+75*x+58", "y^2=81*x^6+13*x^5+72*x^4+61*x^3+77*x^2+77*x+40", "y^2=79*x^6+26*x^5+61*x^4+39*x^3+71*x^2+71*x+80", "y^2=56*x^6+43*x^5+11*x^4+74*x^3+54*x^2+51*x+11", "y^2=29*x^6+3*x^5+22*x^4+65*x^3+25*x^2+19*x+22", "y^2=51*x^6+78*x^5+2*x^4+75*x^3+19*x^2+27*x+5", "y^2=19*x^6+73*x^5+4*x^4+67*x^3+38*x^2+54*x+10", "y^2=67*x^6+48*x^5+2*x^4+68*x^3+75*x^2+33*x+67", "y^2=x^6+6*x^5+81*x^4+82*x^3+77*x^2+32*x+79", "y^2=2*x^6+12*x^5+79*x^4+81*x^3+71*x^2+64*x+75", "y^2=73*x^6+80*x^5+28*x^4+10*x^3+15*x^2+9*x+80", "y^2=63*x^6+77*x^5+56*x^4+20*x^3+30*x^2+18*x+77", "y^2=82*x^6+30*x^5+16*x^4+40*x^3+61*x^2+22*x+66", "y^2=29*x^6+62*x^5+44*x^4+58*x^3+53*x^2+73", "y^2=56*x^6+17*x^5+74*x^4+66*x^3+12*x^2+48*x+32", "y^2=29*x^6+34*x^5+65*x^4+49*x^3+24*x^2+13*x+64", "y^2=10*x^6+33*x^5+7*x^4+15*x^3+28*x^2+65*x+43", "y^2=20*x^6+66*x^5+14*x^4+30*x^3+56*x^2+47*x+3", "y^2=20*x^6+76*x^5+54*x^4+31*x^3+19*x^2+46*x+55", "y^2=54*x^6+28*x^5+2*x^4+40*x^3+5*x^2+45*x+2", "y^2=25*x^6+56*x^5+4*x^4+80*x^3+10*x^2+7*x+4", "y^2=14*x^6+24*x^5+64*x^4+11*x^3+34*x^2+50*x+16", "y^2=28*x^6+48*x^5+45*x^4+22*x^3+68*x^2+17*x+32", "y^2=2*x^6+24*x^5+23*x^4+54*x^3+37*x^2+9*x+26", "y^2=4*x^6+48*x^5+46*x^4+25*x^3+74*x^2+18*x+52", "y^2=71*x^6+44*x^5+52*x^4+42*x^3+79*x^2+19*x+56", "y^2=59*x^6+5*x^5+21*x^4+x^3+75*x^2+38*x+29", "y^2=51*x^6+49*x^5+82*x^4+72*x^3+35*x^2+76*x+69", "y^2=19*x^6+15*x^5+81*x^4+61*x^3+70*x^2+69*x+55", "y^2=11*x^6+79*x^5+21*x^4+69*x^3+69*x^2+53*x+50", "y^2=11*x^6+32*x^5+27*x^4+35*x^3+26*x^2+39*x+76", "y^2=14*x^6+42*x^5+29*x^4+56*x^3+78*x^2+25*x+53", "y^2=28*x^6+x^5+58*x^4+29*x^3+73*x^2+50*x+23", "y^2=77*x^6+52*x^5+36*x^4+30*x^3+25*x^2+81*x+10", "y^2=71*x^6+21*x^5+72*x^4+60*x^3+50*x^2+79*x+20", "y^2=54*x^6+47*x^5+52*x^4+62*x^3+11*x^2+46", "y^2=25*x^6+11*x^5+21*x^4+41*x^3+22*x^2+9", "y^2=3*x^6+56*x^5+43*x^4+13*x^3+6*x^2+22*x+3", "y^2=6*x^6+29*x^5+3*x^4+26*x^3+12*x^2+44*x+6", "y^2=27*x^6+62*x^5+23*x^4+62*x^3+25*x^2+71*x+7", "y^2=10*x^6+17*x^5+49*x^4+3*x^3+81*x^2+5*x+53", "y^2=20*x^6+34*x^5+15*x^4+6*x^3+79*x^2+10*x+23", "y^2=62*x^6+3*x^5+23*x^4+63*x^3+32*x^2+26*x+54", "y^2=41*x^6+6*x^5+46*x^4+43*x^3+64*x^2+52*x+25", "y^2=42*x^6+16*x^5+36*x^4+77*x^3+78*x^2+47*x+28", "y^2=x^6+32*x^5+72*x^4+71*x^3+73*x^2+11*x+56", "y^2=4*x^6+4*x^5+79*x^4+54*x^3+23*x^2+32*x+53", "y^2=8*x^6+8*x^5+75*x^4+25*x^3+46*x^2+64*x+23", "y^2=10*x^6+18*x^5+4*x^4+54*x^3+x^2+15*x+51", "y^2=20*x^6+36*x^5+8*x^4+25*x^3+2*x^2+30*x+19", "y^2=3*x^6+32*x^5+75*x^4+26*x^3+3*x^2+64*x+4", "y^2=60*x^6+65*x^5+19*x^4+46*x^3+70*x^2+11*x", "y^2=75*x^6+65*x^5+21*x^4+11*x^3+12*x^2+79*x+47", "y^2=x^6+3*x^5+82*x^4+61*x^3+51*x^2+37*x+56", "y^2=71*x^6+81*x^5+6*x^4+25*x^3+17*x^2+5*x+23", "y^2=59*x^6+79*x^5+12*x^4+50*x^3+34*x^2+10*x+46", "y^2=26*x^6+6*x^5+65*x^4+8*x^3+61*x^2+3*x+10", "y^2=38*x^6+34*x^5+x^3+73*x^2+25*x+79", "y^2=52*x^6+36*x^5+54*x^4+24*x^2+39*x+18", "y^2=25*x^6+55*x^5+77*x^4+31*x^3+12*x^2+60*x+74", "y^2=50*x^6+27*x^5+71*x^4+62*x^3+24*x^2+37*x+65", "y^2=45*x^6+50*x^5+48*x^4+3*x^3+72*x^2+32*x+6", "y^2=7*x^6+17*x^5+13*x^4+6*x^3+61*x^2+64*x+12", "y^2=67*x^6+69*x^5+69*x^4+34*x^3+71*x^2+57*x+34", "y^2=51*x^6+55*x^5+55*x^4+68*x^3+59*x^2+31*x+68", "y^2=64*x^6+7*x^5+28*x^4+59*x^3+17*x^2+66*x+67", "y^2=45*x^6+14*x^5+56*x^4+35*x^3+34*x^2+49*x+51", "y^2=36*x^6+59*x^5+52*x^4+31*x^3+23*x^2+65*x+71", "y^2=72*x^6+35*x^5+21*x^4+62*x^3+46*x^2+47*x+59", "y^2=34*x^6+25*x^5+65*x^4+8*x^3+55*x^2+14*x+67", "y^2=58*x^6+53*x^5+15*x^3+36*x^2+68*x+67", "y^2=37*x^6+21*x^5+35*x^4+33*x^3+42*x^2+2*x+39", "y^2=74*x^6+42*x^5+70*x^4+66*x^3+x^2+4*x+78", "y^2=43*x^6+20*x^5+48*x^4+47*x^3+11*x^2+65*x+40", "y^2=3*x^6+40*x^5+13*x^4+11*x^3+22*x^2+47*x+80", "y^2=68*x^6+4*x^5+6*x^4+53*x^3+62*x^2+27*x+56", "y^2=24*x^6+29*x^5+21*x^4+3*x^3+66*x^2+22*x+74", "y^2=25*x^6+9*x^5+66*x^4+75*x^3+63*x^2+16*x+28", "y^2=50*x^6+18*x^5+49*x^4+67*x^3+43*x^2+32*x+56", "y^2=70*x^6+22*x^5+67*x^4+40*x^3+76*x^2+38*x+49", "y^2=57*x^6+44*x^5+51*x^4+80*x^3+69*x^2+76*x+15", "y^2=21*x^6+9*x^5+78*x^4+57*x^3+49*x^2+68*x+1", "y^2=69*x^6+14*x^5+38*x^4+17*x^3+6*x^2+70*x+41", "y^2=55*x^6+28*x^5+76*x^4+34*x^3+12*x^2+57*x+82", "y^2=25*x^6+15*x^5+65*x^4+50*x^3+43*x^2+4*x+59", "y^2=50*x^6+30*x^5+47*x^4+17*x^3+3*x^2+8*x+35", "y^2=57*x^6+5*x^5+41*x^4+79*x^3+44*x^2+27*x+43", "y^2=44*x^6+32*x^5+4*x^4+56*x^3+44*x^2+65*x+23", "y^2=5*x^6+64*x^5+8*x^4+29*x^3+5*x^2+47*x+46", "y^2=8*x^6+10*x^5+68*x^4+11*x^3+4*x^2+39*x+70", "y^2=16*x^6+20*x^5+53*x^4+22*x^3+8*x^2+78*x+57", "y^2=60*x^6+65*x^5+x^4+8*x^3+18*x^2+82*x+23", "y^2=37*x^6+47*x^5+2*x^4+16*x^3+36*x^2+81*x+46", "y^2=36*x^6+27*x^5+x^4+22*x^3+41*x^2+54*x+32", "y^2=54*x^6+59*x^5+77*x^4+70*x^3+36*x^2+4*x+81", "y^2=25*x^6+35*x^5+71*x^4+57*x^3+72*x^2+8*x+79", "y^2=22*x^6+37*x^5+53*x^4+29*x^3+13*x^2+9*x+27", "y^2=35*x^6+15*x^5+9*x^4+10*x^3+67*x^2+82*x+48", "y^2=70*x^6+30*x^5+18*x^4+20*x^3+51*x^2+81*x+13", "y^2=26*x^6+29*x^5+62*x^4+17*x^3+43*x^2+53*x+57", "y^2=9*x^6+24*x^5+55*x^4+69*x^3+18*x^2+23*x+17", "y^2=18*x^6+48*x^5+27*x^4+55*x^3+36*x^2+46*x+34", "y^2=81*x^6+60*x^5+57*x^4+57*x^3+24*x^2+37*x+66", "y^2=26*x^6+30*x^5+43*x^4+23*x^3+17*x^2+58*x+50", "y^2=53*x^6+30*x^5+16*x^4+29*x^3+39*x^2+14*x+35", "y^2=23*x^6+60*x^5+32*x^4+58*x^3+78*x^2+28*x+70", "y^2=19*x^6+28*x^5+10*x^4+63*x^3+58*x^2+x+46", "y^2=38*x^6+56*x^5+20*x^4+43*x^3+33*x^2+2*x+9", "y^2=66*x^6+76*x^5+46*x^4+18*x^3+74*x^2+29*x+46", "y^2=61*x^5+44*x^4+80*x^3+6*x^2+30*x+22", "y^2=39*x^5+5*x^4+77*x^3+12*x^2+60*x+44", "y^2=58*x^6+36*x^5+17*x^4+47*x^3+11*x^2+2*x+77", "y^2=51*x^6+23*x^5+21*x^4+39*x^3+26*x^2+62*x+78", "y^2=19*x^6+46*x^5+42*x^4+78*x^3+52*x^2+41*x+73", "y^2=45*x^6+65*x^5+70*x^4+34*x^3+62*x^2+56*x+49", "y^2=7*x^6+47*x^5+57*x^4+68*x^3+41*x^2+29*x+15"], "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": 8, "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": ["2.0.232.1"], "geometric_splitting_field": "2.0.232.1", "geometric_splitting_polynomials": [[58, 0, 1]], "group_structure_count": 3, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 117, "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": 117, "label": "2.83.a_aco", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.215296.3"], "p": 83, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 2], [1, 29, 1, 4], [1, 37, 1, 24]], "poly": [1, 0, -66, 0, 6889], "poly_str": "1 0 -66 0 6889 ", "primitive_models": [], "principal_polarization_count": 139, "q": 83, "real_poly": [1, 0, -232], "simple_distinct": ["2.83.a_aco"], "simple_factors": ["2.83.a_acoA"], "simple_multiplicities": [1], "singular_primes": ["2,-F^2+2*F-V", "5,2*F^2+31*F-41*V-21"], "size": 282, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.215296.3", "splitting_polynomials": [[841, 0, 0, 0, 1]], "twist_count": 6, "twists": [["2.83.au_kg", "2.47458321.bbwu_plzfvy", 4], ["2.83.a_co", "2.47458321.bbwu_plzfvy", 4], ["2.83.u_kg", "2.47458321.bbwu_plzfvy", 4], ["2.83.ak_r", "2.106890007738661124410161.aevtrpzvtk_ktnpqlqfyiyranuqo", 12], ["2.83.k_r", "2.106890007738661124410161.aevtrpzvtk_ktnpqlqfyiyranuqo", 12]], "weak_equivalence_count": 10, "zfv_index": 200, "zfv_index_factorization": [[2, 3], [5, 2]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_pic_size": 96, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 10000, "zfv_singular_count": 4, "zfv_singular_primes": ["2,-F^2+2*F-V", "5,2*F^2+31*F-41*V-21"]}