# Stored data for abelian variety isogeny class 2.67.a_aeo, downloaded from the LMFDB on 11 July 2026.
{"abvar_count": 4372, "abvar_counts": [4372, 19114384, 90458328244, 405868407422976, 1822837806662875732, 8182709148699248123536, 36732225162908423962524148, 164890971619921873680438657024, 740195513856780070694439633562516, 3322737669399523526378452220074535824], "abvar_counts_str": "4372 19114384 90458328244 405868407422976 1822837806662875732 8182709148699248123536 36732225162908423962524148 164890971619921873680438657024 740195513856780070694439633562516 3322737669399523526378452220074535824 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.0785709304621225, 0.921429069537878], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 68, "curve_counts": [68, 4254, 300764, 20141230, 1350125108, 90458274318, 6060711605324, 406067709235294, 27206534396294948, 1822837808773990014], "curve_counts_str": "68 4254 300764 20141230 1350125108 90458274318 6060711605324 406067709235294 27206534396294948 1822837808773990014 ", "curves": ["y^2=11*x^6+38*x^5+59*x^4+30*x^3+66*x^2+32*x+47", "y^2=36*x^6+24*x^5+10*x^4+49*x^3+61*x^2+14*x+41", "y^2=51*x^6+11*x^5+18*x^4+46*x^3+27*x^2+64*x+31", "y^2=50*x^6+x^5+16*x^4+41*x^3+5*x^2+55*x+24", "y^2=51*x^6+4*x^5+52*x^3+33*x+10", "y^2=8*x^6+33*x^5+50*x^4+25*x^3+x^2+59*x+24", "y^2=8*x^6+39*x^5+4*x^4+33*x^2+13*x+45", "y^2=60*x^6+24*x^5+63*x^4+37*x^3+44*x^2+23*x+14", "y^2=53*x^6+48*x^5+59*x^4+7*x^3+21*x^2+46*x+28", "y^2=5*x^6+56*x^5+17*x^4+46*x^3+57*x^2+21*x+59", "y^2=20*x^6+12*x^5+13*x^4+66*x^3+44*x^2+39*x+66", "y^2=40*x^6+15*x^5+56*x^4+2*x^3+27*x^2+65*x+51", "y^2=13*x^6+30*x^5+45*x^4+4*x^3+54*x^2+63*x+35", "y^2=49*x^6+26*x^4+3*x^3+45*x^2+2", "y^2=35*x^6+24*x^5+37*x^4+50*x^2+22*x+34", "y^2=54*x^6+26*x^5+2*x^4+61*x^3+26*x^2+42*x+42", "y^2=41*x^6+52*x^5+4*x^4+55*x^3+52*x^2+17*x+17", "y^2=x^6+31*x^5+26*x^4+11*x^3+19*x^2+24*x+3", "y^2=2*x^6+62*x^5+52*x^4+22*x^3+38*x^2+48*x+6", "y^2=41*x^6+44*x^5+10*x^4+57*x^3+6*x^2+53*x+61", "y^2=15*x^6+21*x^5+20*x^4+47*x^3+12*x^2+39*x+55", "y^2=x^6+24*x^5+15*x^4+65*x^3+32*x^2+53*x+57", "y^2=2*x^6+48*x^5+30*x^4+63*x^3+64*x^2+39*x+47", "y^2=40*x^6+36*x^5+22*x^4+24*x^2+38*x+25", "y^2=28*x^5+53*x^4+47*x^3+4*x^2+33*x+40", "y^2=56*x^5+39*x^4+27*x^3+8*x^2+66*x+13", "y^2=33*x^6+64*x^5+x^4+21*x^3+56*x^2+54*x+7", "y^2=66*x^6+61*x^5+2*x^4+42*x^3+45*x^2+41*x+14", "y^2=29*x^6+26*x^5+3*x^4+45*x^3+25*x^2+4*x+20", "y^2=18*x^6+13*x^5+8*x^4+46*x^3+41*x^2+41*x+43", "y^2=20*x^6+44*x^5+17*x^4+21*x^3+23*x^2+2*x+65", "y^2=40*x^6+21*x^5+34*x^4+42*x^3+46*x^2+4*x+63", "y^2=64*x^6+53*x^5+17*x^4+16*x^3+36*x^2+8*x+50", "y^2=61*x^6+39*x^5+34*x^4+32*x^3+5*x^2+16*x+33", "y^2=33*x^6+16*x^5+11*x^4+17*x^3+35*x^2+23*x+63", "y^2=18*x^6+54*x^5+57*x^4+44*x^3+40*x^2+66*x+59", "y^2=38*x^6+6*x^5+49*x^4+10*x^2+18*x+41", "y^2=54*x^6+58*x^5+59*x^4+9*x^3+53*x^2+52*x+57", "y^2=60*x^6+23*x^5+44*x^4+31*x^2+66*x+36", "y^2=46*x^6+4*x^5+42*x^4+53*x^3+28*x^2+18*x+55", "y^2=25*x^6+8*x^5+17*x^4+39*x^3+56*x^2+36*x+43", "y^2=53*x^6+39*x^5+3*x^4+13*x^2+27*x+42", "y^2=23*x^6+19*x^5+36*x^3+8*x^2+39*x+52", "y^2=46*x^6+38*x^5+5*x^3+16*x^2+11*x+37", "y^2=8*x^6+5*x^5+7*x^4+34*x^3+4*x^2+3*x+64", "y^2=34*x^6+62*x^5+55*x^4+14*x^2+31*x+31", "y^2=7*x^6+22*x^5+37*x^4+30*x^3+51*x^2+14*x+4", "y^2=63*x^6+50*x^5+55*x^4+19*x^3+66*x^2+5*x+29", "y^2=55*x^6+5*x^5+34*x^4+50*x^3+24*x^2+62*x+61", "y^2=43*x^6+10*x^5+x^4+33*x^3+48*x^2+57*x+55", "y^2=40*x^6+10*x^5+48*x^4+60*x^3+62*x^2+56*x+66", "y^2=12*x^6+x^5+5*x^4+52*x^3+65*x^2+35*x+33", "y^2=9*x^6+18*x^5+36*x^4+33*x^3+30*x^2+46*x+8", "y^2=65*x^6+61*x^5+56*x^4+28*x^3+27*x^2+53*x+48", "y^2=64*x^6+25*x^5+32*x^4+54*x^3+17*x^2+10*x+27", "y^2=38*x^6+24*x^5+40*x^4+56*x^2+28*x+63", "y^2=18*x^6+4*x^5+3*x^4+53*x^2+32*x+2", "y^2=61*x^6+60*x^5+2*x^4+14*x^3+21*x^2+25*x+31", "y^2=55*x^6+53*x^5+4*x^4+28*x^3+42*x^2+50*x+62", "y^2=64*x^6+21*x^5+15*x^4+36*x^2+5*x+40", "y^2=41*x^6+54*x^5+15*x^4+6*x^2+53*x+38", "y^2=25*x^6+8*x^5+12*x^4+30*x^3+55*x^2+16*x+22", "y^2=50*x^6+16*x^5+24*x^4+60*x^3+43*x^2+32*x+44", "y^2=31*x^6+62*x^5+43*x^4+14*x^3+9*x^2+15*x+60", "y^2=32*x^6+20*x^5+36*x^4+60*x^3+42*x^2+57*x+26"], "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": 14, "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": ["2.0.7.1"], "geometric_splitting_field": "2.0.7.1", "geometric_splitting_polynomials": [[2, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 65, "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": 65, "label": "2.67.a_aeo", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.784.1"], "p": 67, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, -118, 0, 4489], "poly_str": "1 0 -118 0 4489 ", "primitive_models": [], "q": 67, "real_poly": [1, 0, -252], "simple_distinct": ["2.67.a_aeo"], "simple_factors": ["2.67.a_aeoA"], "simple_multiplicities": [1], "singular_primes": ["2,F^2-2*F+V+2", "3,-11*F+7*V+3"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.784.1", "splitting_polynomials": [[4, 0, -3, 0, 1]], "twist_count": 6, "twists": [["2.67.ai_fu", "2.20151121.aoqm_flswlq", 4], ["2.67.a_eo", "2.20151121.aoqm_flswlq", 4], ["2.67.i_fu", "2.20151121.aoqm_flswlq", 4], ["2.67.ae_abz", "2.8182718904632857144561.bsimiqvbo_bcqxarvzgcvlwqmjm", 12], ["2.67.e_abz", "2.8182718904632857144561.bsimiqvbo_bcqxarvzgcvlwqmjm", 12]], "weak_equivalence_count": 14, "zfv_index": 576, "zfv_index_factorization": [[2, 6], [3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 6, "zfv_plus_index_factorization": [[2, 1], [3, 1]], "zfv_plus_norm": 256, "zfv_singular_count": 4, "zfv_singular_primes": ["2,F^2-2*F+V+2", "3,-11*F+7*V+3"]}