# Stored data for abelian variety isogeny class 2.67.a_ew, downloaded from the LMFDB on 13 February 2026.
{"abvar_count": 4616, "abvar_counts": [4616, 21307456, 90458685704, 405789760562176, 1822837804106497736, 8182773819295053975616, 36732225162887707742473544, 164890952843768078879641190400, 740195513856780001810961674954376, 3322737660079798614453765255773125696], "abvar_counts_str": "4616 21307456 90458685704 405789760562176 1822837804106497736 8182773819295053975616 36732225162887707742473544 164890952843768078879641190400 740195513856780001810961674954376 3322737660079798614453765255773125696 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.44472707612689, 0.55527292387311], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 68, "curve_counts": [68, 4742, 300764, 20137326, 1350125108, 90458989238, 6060711605324, 406067662996318, 27206534396294948, 1822837803661234022], "curve_counts_str": "68 4742 300764 20137326 1350125108 90458989238 6060711605324 406067662996318 27206534396294948 1822837803661234022 ", "curves": ["y^2=20*x^6+23*x^5+17*x^4+34*x^2+42*x+26", "y^2=9*x^6+61*x^5+56*x^4+32*x^3+55*x^2+20*x+29", "y^2=18*x^6+55*x^5+45*x^4+64*x^3+43*x^2+40*x+58", "y^2=2*x^6+43*x^5+49*x^4+36*x^3+50*x^2+53*x+66", "y^2=4*x^6+19*x^5+31*x^4+5*x^3+33*x^2+39*x+65", "y^2=55*x^6+52*x^5+17*x^4+40*x^3+6*x^2+44*x+28", "y^2=43*x^6+37*x^5+34*x^4+13*x^3+12*x^2+21*x+56", "y^2=x^6+11*x^5+4*x^4+19*x^3+58*x^2+20*x+9", "y^2=2*x^6+22*x^5+8*x^4+38*x^3+49*x^2+40*x+18", "y^2=39*x^6+36*x^5+4*x^4+33*x^3+26*x^2+52*x+35", "y^2=11*x^6+5*x^5+8*x^4+66*x^3+52*x^2+37*x+3", "y^2=2*x^6+26*x^5+49*x^4+25*x^3+44*x^2+14*x+57", "y^2=4*x^6+52*x^5+31*x^4+50*x^3+21*x^2+28*x+47", "y^2=58*x^6+59*x^5+45*x^4+7*x^3+64*x^2+3*x+1", "y^2=49*x^6+51*x^5+23*x^4+14*x^3+61*x^2+6*x+2", "y^2=40*x^6+25*x^5+3*x^4+17*x^3+41*x^2+9*x+41", "y^2=13*x^6+50*x^5+6*x^4+34*x^3+15*x^2+18*x+15", "y^2=14*x^6+58*x^5+60*x^4+21*x^3+58*x^2+27*x+5", "y^2=28*x^6+49*x^5+53*x^4+42*x^3+49*x^2+54*x+10", "y^2=38*x^6+54*x^5+38*x^4+9*x^2+52*x+36", "y^2=31*x^6+6*x^5+31*x^4+60*x^3+58*x^2+46*x+7", "y^2=62*x^6+12*x^5+62*x^4+53*x^3+49*x^2+25*x+14", "y^2=10*x^6+25*x^5+39*x^4+35*x^3+32*x^2+44*x+36", "y^2=59*x^6+58*x^5+17*x^4+19*x^3+34*x^2+42*x+32", "y^2=51*x^6+49*x^5+34*x^4+38*x^3+x^2+17*x+64", "y^2=21*x^6+27*x^5+21*x^4+6*x^3+10*x^2+30*x+36", "y^2=42*x^6+54*x^5+42*x^4+12*x^3+20*x^2+60*x+5", "y^2=5*x^6+43*x^5+36*x^4+33*x^3+24*x^2+13*x+32", "y^2=10*x^6+19*x^5+5*x^4+66*x^3+48*x^2+26*x+64", "y^2=65*x^6+63*x^5+21*x^4+43*x^3+57*x^2+12*x+14", "y^2=63*x^6+59*x^5+42*x^4+19*x^3+47*x^2+24*x+28", "y^2=57*x^6+61*x^5+12*x^4+51*x^2+52*x+2", "y^2=47*x^6+55*x^5+24*x^4+35*x^2+37*x+4", "y^2=9*x^6+47*x^5+51*x^4+30*x^3+39*x^2+13*x+66", "y^2=18*x^6+27*x^5+35*x^4+60*x^3+11*x^2+26*x+65", "y^2=26*x^6+2*x^5+50*x^4+11*x^3+45*x^2+42*x+35", "y^2=52*x^6+4*x^5+33*x^4+22*x^3+23*x^2+17*x+3", "y^2=53*x^6+16*x^5+35*x^4+60*x^3+9*x^2+66*x+19", "y^2=39*x^6+32*x^5+3*x^4+53*x^3+18*x^2+65*x+38", "y^2=7*x^6+9*x^5+40*x^4+32*x^3+8*x^2+45*x+50", "y^2=14*x^6+18*x^5+13*x^4+64*x^3+16*x^2+23*x+33", "y^2=10*x^6+64*x^5+7*x^4+36*x^3+29*x^2+55*x+23", "y^2=20*x^6+61*x^5+14*x^4+5*x^3+58*x^2+43*x+46", "y^2=36*x^6+47*x^5+x^4+18*x^3+57*x^2+39*x+18", "y^2=5*x^6+27*x^5+2*x^4+36*x^3+47*x^2+11*x+36", "y^2=17*x^6+55*x^5+14*x^4+10*x^3+28*x^2+56*x+64", "y^2=16*x^6+6*x^5+7*x^4+24*x^3+47*x^2+20*x+42", "y^2=32*x^6+12*x^5+14*x^4+48*x^3+27*x^2+40*x+17", "y^2=22*x^6+59*x^5+31*x^4+56*x^3+52*x^2+56*x+12", "y^2=44*x^6+51*x^5+62*x^4+45*x^3+37*x^2+45*x+24", "y^2=66*x^6+38*x^5+64*x^4+32*x^3+26*x^2+58*x+31", "y^2=34*x^6+53*x^5+x^4+8*x^3+61*x^2+40*x+9", "y^2=33*x^6+54*x^5+46*x^4+42*x^3+16*x^2+26*x+24", "y^2=66*x^6+41*x^5+25*x^4+17*x^3+32*x^2+52*x+48", "y^2=58*x^6+66*x^5+53*x^4+42*x^3+39*x^2+11*x+31", "y^2=49*x^6+65*x^5+39*x^4+17*x^3+11*x^2+22*x+62", "y^2=40*x^6+50*x^5+20*x^4+63*x^3+39*x^2+27*x+7", "y^2=13*x^6+33*x^5+40*x^4+59*x^3+11*x^2+54*x+14", "y^2=11*x^6+21*x^5+50*x^4+16*x^3+25*x^2+56*x+30", "y^2=22*x^6+42*x^5+33*x^4+32*x^3+50*x^2+45*x+60", "y^2=6*x^6+27*x^5+14*x^4+54*x^3+62*x^2+17*x+64", "y^2=25*x^6+52*x^5+50*x^4+14*x^3+34*x^2+33*x+20", "y^2=50*x^6+37*x^5+33*x^4+28*x^3+x^2+66*x+40", "y^2=65*x^6+25*x^5+53*x^4+19*x^3+52*x^2+44*x+57", "y^2=63*x^6+50*x^5+39*x^4+38*x^3+37*x^2+21*x+47", "y^2=5*x^6+8*x^5+66*x^4+49*x^3+25*x^2+2*x+3", "y^2=64*x^6+16*x^5+56*x^4+55*x^3+44*x^2+61*x+4", "y^2=61*x^6+32*x^5+45*x^4+43*x^3+21*x^2+55*x+8", "y^2=x^6+44*x^5+42*x^4+45*x^3+59*x^2+11*x+50", "y^2=2*x^6+21*x^5+17*x^4+23*x^3+51*x^2+22*x+33", "y^2=44*x^6+29*x^5+50*x^4+31*x^3+13*x^2+43*x+58", "y^2=21*x^6+58*x^5+33*x^4+62*x^3+26*x^2+19*x+49", "y^2=18*x^6+34*x^5+59*x^4+44*x^3+32*x^2+11*x+57", "y^2=31*x^6+63*x^5+65*x^4+31*x^3+43*x^2+34*x+38", "y^2=62*x^6+59*x^5+63*x^4+62*x^3+19*x^2+x+9", "y^2=21*x^6+10*x^5+36*x^4+48*x^3+16*x^2+3*x+1", "y^2=42*x^6+20*x^5+5*x^4+29*x^3+32*x^2+6*x+2", "y^2=21*x^6+13*x^5+15*x^4+8*x^3+56*x^2+61*x", "y^2=42*x^6+26*x^5+30*x^4+16*x^3+45*x^2+55*x", "y^2=36*x^6+66*x^5+30*x^4+51*x^3+66*x^2+52*x+63", "y^2=5*x^6+65*x^5+60*x^4+35*x^3+65*x^2+37*x+59", "y^2=23*x^6+x^5+7*x^4+42*x^3+66*x^2+29*x+8", "y^2=46*x^6+2*x^5+14*x^4+17*x^3+65*x^2+58*x+16", "y^2=34*x^6+38*x^5+14*x^4+57*x^3+40*x^2+37*x+14", "y^2=x^6+9*x^5+28*x^4+47*x^3+13*x^2+7*x+28", "y^2=42*x^6+11*x^5+58*x^4+21*x^3+62*x^2+33*x+63", "y^2=17*x^6+22*x^5+49*x^4+42*x^3+57*x^2+66*x+59", "y^2=5*x^6+57*x^5+44*x^4+64*x^3+4*x^2+54*x+60", "y^2=10*x^6+47*x^5+21*x^4+61*x^3+8*x^2+41*x+53", "y^2=56*x^6+22*x^5+38*x^4+14*x^3+2*x^2+46*x+43", "y^2=45*x^6+44*x^5+9*x^4+28*x^3+4*x^2+25*x+19", "y^2=51*x^6+13*x^5+27*x^4+7*x^3+64*x^2+50*x+4", "y^2=35*x^6+26*x^5+54*x^4+14*x^3+61*x^2+33*x+8", "y^2=9*x^6+26*x^5+21*x^4+17*x^3+5*x^2+52*x+38", "y^2=18*x^6+52*x^5+42*x^4+34*x^3+10*x^2+37*x+9", "y^2=41*x^6+27*x^5+13*x^4+50*x^3+13*x^2+53*x+63", "y^2=15*x^6+54*x^5+26*x^4+33*x^3+26*x^2+39*x+59", "y^2=49*x^6+25*x^5+45*x^4+58*x^3+59*x^2+21*x+8", "y^2=12*x^6+37*x^5+64*x^4+62*x^3+45*x^2+49*x+26", "y^2=24*x^6+7*x^5+61*x^4+57*x^3+23*x^2+31*x+52", "y^2=39*x^6+19*x^5+47*x^4+44*x^3+53*x^2+14*x+42", "y^2=11*x^6+38*x^5+27*x^4+21*x^3+39*x^2+28*x+17", "y^2=28*x^6+58*x^5+53*x^4+53*x^3+57*x^2+65*x+57", "y^2=56*x^6+49*x^5+39*x^4+39*x^3+47*x^2+63*x+47", "y^2=12*x^6+37*x^5+17*x^4+55*x^3+6*x^2+39*x+40", "y^2=24*x^6+7*x^5+34*x^4+43*x^3+12*x^2+11*x+13"], "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": 4, "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": ["2.0.520.1"], "geometric_splitting_field": "2.0.520.1", "geometric_splitting_polynomials": [[130, 0, 1]], "group_structure_count": 3, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 106, "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": 106, "label": "2.67.a_ew", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 8, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.1081600.8"], "p": 67, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 8], [1, 23, 1, 16], [1, 31, 1, 16]], "poly": [1, 0, 126, 0, 4489], "poly_str": "1 0 126 0 4489 ", "primitive_models": [], "principal_polarization_count": 112, "q": 67, "real_poly": [1, 0, -8], "simple_distinct": ["2.67.a_ew"], "simple_factors": ["2.67.a_ewA"], "simple_multiplicities": [1], "singular_primes": ["2,F^2+F-2"], "size": 176, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.1081600.8", "splitting_polynomials": [[1089, 0, 64, 0, 1]], "twist_count": 4, "twists": [["2.67.a_aew", "2.20151121.aukq_hkigws", 4], ["2.67.ae_i", "2.406067677556641.abfwkym_gdivspmkluc", 8], ["2.67.e_i", "2.406067677556641.abfwkym_gdivspmkluc", 8]], "weak_equivalence_count": 5, "zfv_index": 8, "zfv_index_factorization": [[2, 3]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_pic_size": 64, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 67600, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F^2+F-2"]}