# Stored data for abelian variety isogeny class 2.67.aq_hq, downloaded from the LMFDB on 11 March 2026.
{"abvar_count": 3600, "abvar_counts": [3600, 20793600, 91119459600, 406232087040000, 1822727617106490000, 8182610411198994950400, 36732200151762564618963600, 164890977981241981029949440000, 740195531683807032766551690723600, 3322737665476204444432706950273440000], "abvar_counts_str": "3600 20793600 91119459600 406232087040000 1822727617106490000 8182610411198994950400 36732200151762564618963600 164890977981241981029949440000 740195531683807032766551690723600 3322737665476204444432706950273440000 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.337479373806535, 0.337479373806535], "center_dim": 2, "curve_count": 52, "curve_counts": [52, 4630, 302956, 20159278, 1350043492, 90457182790, 6060707478556, 406067724900958, 27206535051542932, 1822837806621676150], "curve_counts_str": "52 4630 302956 20159278 1350043492 90457182790 6060707478556 406067724900958 27206535051542932 1822837806621676150 ", "curves": ["y^2=54*x^6+10*x^5+x^4+28*x^3+26*x^2+60*x+49", "y^2=3*x^6+39*x^5+54*x^4+41*x^3+54*x^2+39*x+3", "y^2=3*x^6+35*x^5+66*x^4+35*x^3+10*x^2+9*x+27", "y^2=25*x^6+65*x^5+x^4+54*x^3+x^2+65*x+25", "y^2=39*x^6+24*x^5+58*x^4+57*x^3+46*x^2+19*x+19", "y^2=32*x^6+30*x^5+66*x^4+27*x^3+24*x^2+11*x+15", "y^2=51*x^6+54*x^5+19*x^4+28*x^3+19*x^2+54*x+51", "y^2=43*x^6+2*x^5+61*x^4+22*x^3+61*x^2+2*x+43", "y^2=27*x^6+9*x^5+36*x^4+66*x^3+53*x^2+5*x+53", "y^2=50*x^6+29*x^5+63*x^4+38*x^3+63*x^2+29*x+50", "y^2=24*x^6+51*x^5+18*x^4+14*x^3+18*x^2+51*x+24", "y^2=49*x^6+x^5+15*x^4+8*x^3+60*x^2+16*x+54", "y^2=66*x^6+47*x^5+3*x^4+64*x^3+8*x^2+29*x+25", "y^2=5*x^6+5*x^5+61*x^4+56*x^3+61*x^2+5*x+5", "y^2=4*x^6+5*x^5+11*x^4+3*x^3+14*x^2+34*x+38", "y^2=4*x^6+24*x^5+14*x^4+x^3+14*x^2+24*x+4", "y^2=46*x^6+61*x^5+23*x^4+27*x^3+14*x^2+34*x+20", "y^2=54*x^6+23*x^5+7*x^4+11*x^3+17*x^2+66*x+63", "y^2=x^6+56*x^3+9", "y^2=16*x^6+63*x^5+5*x^4+53*x^3+5*x^2+63*x+16", "y^2=46*x^6+37*x^5+3*x^4+23*x^3+3*x^2+37*x+46", "y^2=41*x^6+5*x^5+4*x^4+13*x^3+54*x^2+21*x+53", "y^2=66*x^6+59*x^5+53*x^4+9*x^3+20*x^2+33*x+2", "y^2=62*x^6+37*x^5+35*x^4+32*x^3+23*x^2+4*x+40", "y^2=2*x^6+40*x^5+24*x^4+41*x^3+27*x^2+52*x+65", "y^2=59*x^6+48*x^4+48*x^2+59", "y^2=59*x^6+39*x^5+8*x^4+53*x^3+8*x^2+39*x+59", "y^2=38*x^6+25*x^5+50*x^4+19*x^3+3*x^2+49*x+63", "y^2=43*x^6+31*x^5+33*x^4+66*x^3+14*x^2+23*x+4", "y^2=48*x^6+16*x^5+7*x^4+25*x^3+12*x^2+27*x+6", "y^2=8*x^6+35*x^4+35*x^2+8", "y^2=2*x^6+43*x^5+48*x^4+65*x^3+13*x^2+29*x+14", "y^2=x^6+38*x^5+5*x^4+26*x^3+5*x^2+38*x+1", "y^2=x^6+33*x^5+34*x^4+59*x^3+36*x^2+29*x+41", "y^2=44*x^6+27*x^5+27*x^4+44*x^2+32*x+28", "y^2=49*x^6+39*x^4+39*x^2+49", "y^2=13*x^6+61*x^5+35*x^4+38*x^3+54*x^2+65*x+53", "y^2=2*x^6+31*x^5+41*x^4+34*x^3+x^2+41*x+2", "y^2=66*x^6+62*x^5+40*x^4+14*x^3+12*x^2+65*x+23", "y^2=58*x^6+34*x^5+45*x^4+49*x^3+47*x^2+56*x+54", "y^2=45*x^6+37*x^5+5*x^4+3*x^3+34*x^2+2*x+45", "y^2=21*x^6+40*x^5+51*x^4+38*x^3+10*x^2+52*x+61", "y^2=36*x^6+25*x^5+18*x^4+66*x^3+63*x^2+55*x+36", "y^2=32*x^6+49*x^5+41*x^4+42*x^3+41*x^2+49*x+32", "y^2=58*x^6+61*x^4+61*x^2+58", "y^2=64*x^6+13*x^5+6*x^4+26*x^3+47*x^2+53*x+48", "y^2=9*x^6+30*x^4+30*x^2+9", "y^2=x^6+x^3+64", "y^2=16*x^6+62*x^5+7*x^4+19*x^3+58*x^2+56*x+16", "y^2=32*x^6+22*x^5+14*x^4+57*x^3+49*x^2+35*x+32", "y^2=57*x^6+29*x^5+43*x^4+50*x^3+49*x^2+52*x+47", "y^2=x^6+51*x^5+66*x^4+54*x^3+66*x^2+51*x+1", "y^2=53*x^6+49*x^5+54*x^4+9*x^3+11*x^2+37*x+32", "y^2=14*x^6+41*x^5+66*x^4+9*x^3+12*x^2+57*x+30", "y^2=55*x^6+59*x^5+8*x^4+33*x^3+8*x^2+59*x+55", "y^2=44*x^6+34*x^5+47*x^4+41*x^3+15*x^2+11*x+19", "y^2=26*x^6+6*x^5+13*x^4+29*x^3+49*x^2+66*x+41", "y^2=x^6+16*x^3+9", "y^2=8*x^6+62*x^5+37*x^4+59*x^3+62*x^2+65*x+5", "y^2=63*x^6+11*x^5+66*x^4+17*x^3+3*x^2+32*x+41", "y^2=6*x^6+58*x^5+39*x^4+48*x^3+39*x^2+58*x+6", "y^2=29*x^6+27*x^5+58*x^4+57*x^3+63*x^2+49*x+48", "y^2=31*x^5+14*x^4+54*x^3+14*x^2+31*x", "y^2=8*x^6+43*x^4+43*x^2+8", "y^2=10*x^6+12*x^5+45*x^4+3*x^3+57*x^2+11*x+29", "y^2=52*x^6+30*x^5+6*x^4+8*x^3+31*x^2+16*x+60", "y^2=x^6+36*x^3+24", "y^2=2*x^6+47*x^5+58*x^4+64*x^3+13*x^2+52*x+39", "y^2=x^6+60*x^5+25*x^4+65*x^3+26*x^2+8*x+24", "y^2=65*x^6+8*x^5+36*x^4+36*x^3+65*x^2+48*x+23", "y^2=25*x^6+45*x^5+21*x^4+11*x^3+21*x^2+45*x+25", "y^2=34*x^6+42*x^5+43*x^4+45*x^3+36*x^2+22*x+34", "y^2=39*x^6+16*x^5+26*x^4+2*x^3+56*x^2+10*x+19", "y^2=28*x^6+33*x^5+24*x^4+21*x^3+24*x^2+33*x+28", "y^2=26*x^6+8*x^5+8*x^4+11*x^3+22*x^2+44*x+57", "y^2=13*x^6+2*x^5+22*x^4+45*x^3+59*x^2+13*x+18"], "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": ["2.0.51.1"], "geometric_splitting_field": "2.0.51.1", "geometric_splitting_polynomials": [[13, -1, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 76, "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": 76, "label": "2.67.aq_hq", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2, 3, 5], "number_fields": ["2.0.51.1"], "p": 67, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -16, 198, -1072, 4489], "poly_str": "1 -16 198 -1072 4489 ", "primitive_models": [], "q": 67, "real_poly": [1, -16, 64], "simple_distinct": ["1.67.ai"], "simple_factors": ["1.67.aiA", "1.67.aiB"], "simple_multiplicities": [2], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.51.1", "splitting_polynomials": [[13, -1, 1]], "twist_count": 6, "twists": [["2.67.a_cs", "2.4489.fk_unu", 2], ["2.67.q_hq", "2.4489.fk_unu", 2], ["2.67.i_ad", "2.300763.dgi_dyoug", 3], ["2.67.a_acs", "2.20151121.mbs_eupfkw", 4], ["2.67.ai_ad", "2.90458382169.acqgga_cphvdqkpy", 6]]}