# Stored data for abelian variety isogeny class 2.67.ak_gd, downloaded from the LMFDB on 25 April 2026.
{"abvar_count": 3969, "abvar_counts": [3969, 21150801, 90989102736, 405950728871961, 1822639411765966689, 8182687629038940815616, 36732274357176124572560841, 164890984642924810667720675625, 740195507733007123058257896906384, 3322737651865866546978173550664009521], "abvar_counts_str": "3969 21150801 90989102736 405950728871961 1822639411765966689 8182687629038940815616 36732274357176124572560841 164890984642924810667720675625 740195507733007123058257896906384 3322737651865866546978173550664009521 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.401201937998485, 0.401201937998485], "center_dim": 2, "curve_count": 58, "curve_counts": [58, 4708, 302524, 20145316, 1349978158, 90458036422, 6060719722234, 406067741306308, 27206534171210308, 1822837799155110628], "curve_counts_str": "58 4708 302524 20145316 1349978158 90458036422 6060719722234 406067741306308 27206534171210308 1822837799155110628 ", "curves": ["y^2=46*x^6+58*x^5+48*x^4+10*x^3+48*x^2+58*x+46", "y^2=47*x^6+63*x^5+x^4+15*x^3+33*x^2+56*x+48", "y^2=25*x^6+40*x^5+48*x^4+12*x^3+40*x^2+35*x+31", "y^2=12*x^6+42*x^4+66*x^3+42*x^2+12", "y^2=41*x^6+5*x^4+39*x^3+5*x^2+41", "y^2=46*x^6+6*x^5+58*x^4+63*x^3+58*x^2+6*x+46", "y^2=30*x^6+11*x^5+37*x^4+63*x^3+37*x^2+11*x+30", "y^2=13*x^6+14*x^5+65*x^4+15*x^3+65*x^2+14*x+13", "y^2=20*x^6+30*x^5+47*x^4+58*x^3+47*x^2+30*x+20", "y^2=21*x^6+12*x^5+3*x^4+57*x^3+29*x^2+8*x+41", "y^2=20*x^6+19*x^5+39*x^4+37*x^3+39*x^2+19*x+20", "y^2=24*x^6+20*x^5+43*x^4+52*x^3+43*x^2+20*x+24", "y^2=15*x^6+8*x^5+50*x^4+36*x^3+23*x^2+66*x+45", "y^2=28*x^6+49*x^5+47*x^4+16*x^3+34*x^2+31*x+30", "y^2=51*x^6+28*x^5+45*x^4+42*x^3+45*x^2+28*x+51", "y^2=63*x^6+47*x^5+64*x^4+13*x^3+64*x^2+47*x+63", "y^2=7*x^6+22*x^5+55*x^4+65*x^3+55*x^2+22*x+7", "y^2=46*x^6+12*x^5+9*x^4+27*x^3+42*x^2+35*x+56", "y^2=23*x^6+37*x^5+26*x^4+51*x^3+61*x^2+23*x+27", "y^2=24*x^6+62*x^5+59*x^4+53*x^3+59*x^2+62*x+24", "y^2=9*x^6+51*x^5+53*x^4+21*x^3+53*x^2+51*x+9", "y^2=45*x^6+26*x^5+49*x^4+30*x^3+49*x^2+26*x+45", "y^2=8*x^6+61*x^5+11*x^4+31*x^3+11*x^2+61*x+8", "y^2=11*x^6+49*x^5+35*x^4+53*x^3+65*x^2+12*x+16", "y^2=x^6+x^3+25", "y^2=x^6+35*x^3+62", "y^2=32*x^6+35*x^5+25*x^4+11*x^3+42*x^2+54*x+17", "y^2=3*x^6+64*x^5+13*x^4+66*x^3+65*x^2+57*x+41", "y^2=31*x^6+3*x^5+24*x^4+64*x^3+24*x^2+3*x+31", "y^2=52*x^6+47*x^5+2*x^4+19*x^3+2*x^2+47*x+52", "y^2=63*x^6+28*x^5+37*x^4+18*x^3+32*x^2+22*x+20", "y^2=14*x^6+19*x^5+16*x^4+40*x^3+46*x^2+59*x+36", "y^2=34*x^6+61*x^5+52*x^4+27*x^3+32*x^2+43*x+14", "y^2=47*x^6+13*x^5+30*x^4+51*x^3+30*x^2+13*x+47", "y^2=4*x^6+11*x^5+55*x^2+26*x+3", "y^2=x^6+65*x^3+59", "y^2=x^6+19*x^3+25", "y^2=6*x^6+40*x^5+55*x^4+19*x^3+31*x^2+10*x+30", "y^2=60*x^6+13*x^5+11*x^4+37*x^3+31*x^2+59*x+3", "y^2=11*x^6+12*x^5+54*x^4+61*x^3+54*x^2+12*x+11", "y^2=55*x^6+58*x^5+12*x^4+48*x^3+12*x^2+58*x+55", "y^2=39*x^6+60*x^5+17*x^4+11*x^3+26*x^2+34*x+20", "y^2=55*x^6+48*x^5+38*x^4+3*x^3+38*x^2+48*x+55"], "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": ["2.0.3.1"], "geometric_splitting_field": "2.0.3.1", "geometric_splitting_polynomials": [[1, -1, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 43, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": false, "jacobian_count": 43, "label": "2.67.ak_gd", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [3, 7], "number_fields": ["2.0.3.1"], "p": 67, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -10, 159, -670, 4489], "poly_str": "1 -10 159 -670 4489 ", "primitive_models": [], "q": 67, "real_poly": [1, -10, 25], "simple_distinct": ["1.67.af"], "simple_factors": ["1.67.afA", "1.67.afB"], "simple_multiplicities": [2], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.3.1", "splitting_polynomials": [[1, -1, 1]], "twist_count": 24, "twists": [["2.67.a_ef", "2.4489.ik_bewh", 2], ["2.67.k_gd", "2.4489.ik_bewh", 2], ["2.67.aw_jv", "2.300763.cps_dahkg", 3], ["2.67.aq_hh", "2.300763.cps_dahkg", 3], ["2.67.f_abq", "2.300763.cps_dahkg", 3], ["2.67.l_cc", "2.300763.cps_dahkg", 3], ["2.67.bg_pa", "2.300763.cps_dahkg", 3], ["2.67.a_aef", "2.20151121.aipi_ecqnhj", 4], ["2.67.abg_pa", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.abb_ly", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.av_ig", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.al_cc", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.ag_db", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.af_abq", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.a_aes", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.a_n", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.g_db", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.q_hh", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.v_ig", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.w_jv", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.bb_ly", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.a_an", "2.8182718904632857144561.blpvfkjfw_xjhkhpawvmpnyyig", 12], ["2.67.a_es", "2.8182718904632857144561.blpvfkjfw_xjhkhpawvmpnyyig", 12]]}