# Stored data for abelian variety isogeny class 2.61.au_io, downloaded from the LMFDB on 22 September 2025.
{"abvar_count": 2704, "abvar_counts": [2704, 14017536, 51898307344, 191900067840000, 713374923911023504, 2654324766268399051776, 9876810500678400133198864, 36751685911488957592535040000, 136753052995011561291989736156304, 508858111517299825401742886889071616], "abvar_counts_str": "2704 14017536 51898307344 191900067840000 713374923911023504 2654324766268399051776 9876810500678400133198864 36751685911488957592535040000 136753052995011561291989736156304 508858111517299825401742886889071616 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.278857938376305, 0.278857938376305], "center_dim": 2, "curve_count": 42, "curve_counts": [42, 3766, 228642, 13859758, 844634202, 51519904486, 3142735825362, 191707271553118, 11694146106042762, 713342914323062806], "curve_counts_str": "42 3766 228642 13859758 844634202 51519904486 3142735825362 191707271553118 11694146106042762 713342914323062806 ", "curves": ["y^2=6*x^6+58*x^5+35*x^3+58*x^2+7*x+21", "y^2=32*x^6+23*x^5+46*x^4+39*x^3+13*x^2+33*x+35", "y^2=16*x^6+20*x^5+45*x^4+24*x^3+39*x^2+34*x+13", "y^2=28*x^6+41*x^5+18*x^4+28*x^3+18*x^2+41*x+28", "y^2=47*x^6+25*x^4+25*x^2+47", "y^2=52*x^6+53*x^4+53*x^2+52", "y^2=24*x^6+10*x^4+10*x^2+24", "y^2=59*x^6+18*x^4+18*x^2+59", "y^2=51*x^6+24*x^5+3*x^4+49*x^3+15*x^2+51*x+31", "y^2=17*x^6+45*x^4+45*x^2+17", "y^2=43*x^6+22*x^5+5*x^4+18*x^3+31*x^2+18*x+18", "y^2=7*x^6+29*x^5+5*x^4+8*x^3+x^2+28*x+43", "y^2=14*x^6+33*x^5+42*x^4+3*x^3+51*x^2+34*x+16", "y^2=2*x^6+38*x^3+54", "y^2=40*x^6+24*x^5+27*x^4+11*x^3+25*x^2+2*x+43", "y^2=27*x^6+39*x^5+19*x^4+32*x^3+19*x^2+39*x+27", "y^2=32*x^6+32*x^5+55*x^4+8*x^3+50*x^2+28*x+18", "y^2=39*x^6+32*x^5+9*x^4+12*x^3+60*x^2+26*x+13", "y^2=17*x^6+53*x^5+36*x^4+38*x^3+36*x^2+53*x+17", "y^2=2*x^6+2*x^3+43", "y^2=48*x^6+41*x^5+49*x^4+2*x^3+25*x^2+3*x+15", "y^2=43*x^6+2*x^5+4*x^4+x^3+57*x^2+51*x+21", "y^2=23*x^6+15*x^4+15*x^2+23", "y^2=46*x^6+33*x^5+58*x^4+17*x^3+25*x^2+10*x+55", "y^2=41*x^6+27*x^5+21*x^4+12*x^3+12*x^2+14*x+46", "y^2=6*x^6+56*x^5+47*x^4+54*x^3+34*x^2+34*x+59", "y^2=2*x^6+2*x^3+6", "y^2=38*x^6+38*x^5+42*x^4+11*x^3+42*x^2+38*x+38", "y^2=23*x^6+28*x^5+11*x^4+10*x^3+11*x^2+28*x+23", "y^2=21*x^6+5*x^5+55*x^4+26*x^3+32*x^2+27*x+54", "y^2=3*x^6+40*x^5+2*x^4+50*x^3+55*x^2+55*x+41", "y^2=2*x^6+8*x^3+6", "y^2=2*x^6+28*x^3+59", "y^2=51*x^6+27*x^5+35*x^4+21*x^3+51*x^2+52*x+31", "y^2=18*x^6+42*x^5+15*x^4+9*x^3+57*x^2+x+18", "y^2=20*x^6+15*x^5+16*x^4+50*x^3+46*x^2+22*x+3", "y^2=33*x^6+26*x^5+23*x^4+4*x^3+37*x^2+32*x+38", "y^2=35*x^6+4*x^5+15*x^4+34*x^3+9*x^2+60*x+10", "y^2=28*x^6+26*x^5+25*x^4+15*x^3+49*x^2+30*x+53", "y^2=46*x^6+55*x^5+6*x^4+45*x^3+6*x^2+55*x+46", "y^2=2*x^6+35*x^3+59", "y^2=17*x^6+37*x^5+38*x^4+25*x^3+55*x^2+31*x+44", "y^2=18*x^6+46*x^5+38*x^4+3*x^3+54*x^2+52*x+7", "y^2=32*x^6+34*x^5+11*x^4+50*x^3+24*x^2+58*x+17", "y^2=33*x^6+55*x^5+13*x^4+39*x^3+41*x^2+13*x+21", "y^2=26*x^5+48*x^4+39*x^3+14*x^2+2*x", "y^2=59*x^6+53*x^5+16*x^4+46*x^3+57*x^2+30*x+21", "y^2=38*x^6+2*x^5+60*x^4+12*x^3+12*x^2+44*x+33", "y^2=32*x^6+17*x^5+48*x^4+18*x^3+9*x^2+28*x+35"], "dim1_distinct": 1, "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, "g": 2, "galois_groups": ["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": 1, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.4.1"], "geometric_splitting_field": "2.0.4.1", "geometric_splitting_polynomials": [[1, 0, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 49, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": false, "jacobian_count": 49, "label": "2.61.au_io", "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"], "p": 61, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -20, 222, -1220, 3721], "poly_str": "1 -20 222 -1220 3721 ", "primitive_models": [], "q": 61, "real_poly": [1, -20, 100], "simple_distinct": ["1.61.ak"], "simple_factors": ["1.61.akA", "1.61.akB"], "simple_multiplicities": [2], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.4.1", "splitting_polynomials": [[1, 0, 1]], "twist_count": 16, "twists": [["2.61.a_w", "2.3721.bs_lsw", 2], ["2.61.u_io", "2.3721.bs_lsw", 2], ["2.61.k_bn", "2.226981.clw_cnaqg", 3], ["2.61.ay_kg", "2.13845841.upg_gkocao", 4], ["2.61.aw_ji", "2.13845841.upg_gkocao", 4], ["2.61.ac_c", "2.13845841.upg_gkocao", 4], ["2.61.a_aw", "2.13845841.upg_gkocao", 4], ["2.61.c_c", "2.13845841.upg_gkocao", 4], ["2.61.w_ji", "2.13845841.upg_gkocao", 4], ["2.61.y_kg", "2.13845841.upg_gkocao", 4], ["2.61.ak_bn", "2.51520374361.abatce_tsgazlgg", 6], ["2.61.a_aeq", "2.191707312997281.admrzyi_ftsiajznsyw", 8], ["2.61.a_eq", "2.191707312997281.admrzyi_ftsiajznsyw", 8], ["2.61.am_df", "2.2654348974297586158321.lxttuvvw_enufrjizegwqykmg", 12], ["2.61.m_df", "2.2654348974297586158321.lxttuvvw_enufrjizegwqykmg", 12]]}