# Stored data for abelian variety isogeny class 2.67.ay_ks, downloaded from the LMFDB on 28 October 2025.
{"abvar_count": 3136, "abvar_counts": [3136, 20070400, 90870896704, 406425600000000, 1823001737727585856, 8182743087975530905600, 36732195303049634047557184, 164890927475519732121600000000, 740195497687818622026058032986176, 3322737658111325782170521755740160000], "abvar_counts_str": "3136 20070400 90870896704 406425600000000 1823001737727585856 8182743087975530905600 36732195303049634047557184 164890927475519732121600000000 740195497687818622026058032986176 3322737658111325782170521755740160000 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.23811171333255, 0.23811171333255], "center_dim": 2, "curve_count": 44, "curve_counts": [44, 4470, 302132, 20168878, 1350246524, 90458649510, 6060706678532, 406067600523358, 27206533801990604, 1822837802581339350], "curve_counts_str": "44 4470 302132 20168878 1350246524 90458649510 6060706678532 406067600523358 27206533801990604 1822837802581339350 ", "curves": ["y^2=8*x^6+10*x^5+42*x^4+35*x^3+4*x^2+35*x+17", "y^2=58*x^6+24*x^5+28*x^4+5*x^3+28*x^2+24*x+58", "y^2=16*x^5+38*x^4+40*x^3+61*x^2+21*x", "y^2=19*x^5+32*x^4+16*x^3+32*x^2+19*x", "y^2=18*x^6+29*x^5+65*x^4+25*x^3+65*x^2+29*x+18", "y^2=29*x^6+54*x^5+19*x^4+17*x^3+15*x^2+55*x+29", "y^2=66*x^6+21*x^4+21*x^2+66", "y^2=40*x^6+42*x^5+50*x^4+47*x^3+7*x^2+31*x+22", "y^2=21*x^6+34*x^5+42*x^4+16*x^3+42*x^2+34*x+21", "y^2=3*x^6+22*x^5+28*x^4+43*x^3+28*x^2+22*x+3", "y^2=55*x^6+41*x^5+44*x^4+32*x^3+44*x^2+41*x+55", "y^2=2*x^6+30*x^5+62*x^4+28*x^3+4*x^2+46*x+44", "y^2=11*x^6+28*x^4+28*x^2+11", "y^2=36*x^6+16*x^5+15*x^4+30*x^3+59*x^2+47*x+26", "y^2=42*x^6+66*x^4+66*x^2+42", "y^2=x^6+34*x^5+17*x^4+4*x^3+22*x^2+53*x+15", "y^2=32*x^6+7*x^5+15*x^4+3*x^3+15*x^2+7*x+32", "y^2=30*x^6+57*x^5+66*x^4+61*x^3+7*x^2+46*x+28", "y^2=2*x^6+26*x^5+52*x^4+65*x^3+52*x^2+26*x+2", "y^2=48*x^6+4*x^5+55*x^4+13*x^3+51*x^2+39*x+1", "y^2=12*x^6+62*x^5+34*x^4+49*x^3+34*x^2+62*x+12", "y^2=38*x^6+24*x^5+43*x^4+19*x^3+12*x^2+41*x+35", "y^2=40*x^6+51*x^5+20*x^4+43*x^3+20*x^2+51*x+40", "y^2=10*x^6+45*x^5+46*x^4+64*x^3+53*x^2+5*x+24", "y^2=42*x^6+29*x^5+21*x^4+19*x^3+21*x^2+29*x+42", "y^2=45*x^6+54*x^5+4*x^4+35*x^3+17*x^2+29*x+5", "y^2=45*x^6+26*x^5+53*x^4+38*x^3+53*x^2+26*x+45", "y^2=45*x^6+51*x^5+18*x^4+23*x^3+27*x^2+31*x+43", "y^2=62*x^6+50*x^5+50*x^4+20*x^3+9*x^2+32*x+39", "y^2=11*x^6+51*x^5+63*x^4+36*x^3+44*x^2+7*x+32", "y^2=42*x^6+21*x^5+22*x^4+51*x^3+56*x^2+22*x+45", "y^2=x^6+6*x^5+11*x^4+26*x^3+11*x^2+6*x+1", "y^2=35*x^6+42*x^4+42*x^2+35", "y^2=34*x^6+33*x^5+21*x^4+17*x^3+21*x^2+33*x+34", "y^2=41*x^6+17*x^5+49*x^4+24*x^3+56*x^2+14*x+11", "y^2=66*x^6+13*x^5+37*x^4+8*x^3+24*x^2+11*x+45", "y^2=19*x^6+47*x^4+47*x^2+19", "y^2=3*x^6+x^4+x^2+3", "y^2=54*x^6+15*x^5+46*x^4+66*x^3+46*x^2+15*x+54"], "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": ["2.0.31.1"], "geometric_splitting_field": "2.0.31.1", "geometric_splitting_polynomials": [[8, -1, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 39, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": false, "jacobian_count": 39, "label": "2.67.ay_ks", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.31.1"], "p": 67, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -24, 278, -1608, 4489], "poly_str": "1 -24 278 -1608 4489 ", "primitive_models": [], "q": 67, "real_poly": [1, -24, 144], "simple_distinct": ["1.67.am"], "simple_factors": ["1.67.amA", "1.67.amB"], "simple_multiplicities": [2], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.31.1", "splitting_polynomials": [[8, -1, 1]], "twist_count": 6, "twists": [["2.67.a_ak", "2.4489.au_nle", 2], ["2.67.y_ks", "2.4489.au_nle", 2], ["2.67.m_cz", "2.300763.caq_civyc", 3], ["2.67.a_k", "2.20151121.bagy_karmru", 4], ["2.67.am_cz", "2.90458382169.pfmi_ytmtsumo", 6]]}