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av_fq_isog • Show schema
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{'abvar_count': 1528, 'abvar_counts': [1528, 2848192, 4723428472, 7997221854208, 13426311081824248, 22563401884526469568, 37929392664166652290168, 63759043041500168962818048, 107178910718734178086144690168, 180167781640476454609966683562432], 'abvar_counts_str': '1528 2848192 4723428472 7997221854208 13426311081824248 22563401884526469568 37929392664166652290168 63759043041500168962818048 107178910718734178086144690168 180167781640476454609966683562432 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.194660287865938, 0.669029747545703], 'center_dim': 4, 'cohen_macaulay_max': 2, 'curve_count': 38, 'curve_counts': [38, 1694, 68534, 2830110, 115887718, 4750085630, 194755123510, 7984926747838, 327381872543270, 13422659212113374], 'curve_counts_str': '38 1694 68534 2830110 115887718 4750085630 194755123510 7984926747838 327381872543270 13422659212113374 ', 'curves': ['y^2=21*x^6+29*x^5+17*x^4+37*x^2+32*x+15', 'y^2=10*x^6+17*x^5+26*x^4+11*x^3+4*x^2+13*x+20', 'y^2=4*x^6+38*x^5+11*x^4+35*x^3+14*x^2+35*x+9', 'y^2=27*x^6+17*x^5+14*x^4+20*x^3+27*x^2+2*x+4', 'y^2=22*x^6+36*x^5+27*x^4+3*x^3+39*x^2+39*x+16', 'y^2=7*x^6+33*x^5+39*x^4+16*x^3+14*x^2+34*x+18', 'y^2=4*x^6+15*x^5+3*x^4+18*x^3+2*x^2+7*x+11', 'y^2=2*x^6+4*x^5+7*x^4+2*x^3+26*x^2+29*x+34', 'y^2=40*x^6+34*x^5+18*x^4+7*x^3+21*x^2+38*x', 'y^2=17*x^6+9*x^5+9*x^4+30*x^3+40*x^2+13*x+8', 'y^2=2*x^6+22*x^5+11*x^4+33*x^3+25*x^2+5*x+31', 'y^2=12*x^6+38*x^5+39*x^4+29*x^3+6*x^2+10*x+16', 'y^2=28*x^6+11*x^5+22*x^4+31*x^3+36*x^2+5*x+19', 'y^2=5*x^6+5*x^5+37*x^4+37*x^3+27*x^2+6*x', 'y^2=9*x^6+39*x^5+32*x^4+26*x^3+34*x^2+19*x+26', 'y^2=9*x^6+36*x^5+2*x^4+3*x^3+19*x^2+3*x+36', 'y^2=29*x^6+37*x^5+20*x^4+29*x^3+31*x^2+32*x+17', 'y^2=33*x^6+33*x^5+33*x^4+17*x^3+7*x^2+23*x+29', 'y^2=31*x^6+4*x^5+2*x^4+30*x^3+x^2+8*x+32', 'y^2=40*x^6+28*x^5+4*x^4+15*x^3+6*x^2+7*x+34', 'y^2=11*x^6+27*x^5+x^4+21*x^3+2*x^2+7*x+29', 'y^2=19*x^6+11*x^4+28*x^3+17*x^2+8*x+29', 'y^2=9*x^6+33*x^5+5*x^4+10*x^3+27*x^2+16*x+15', 'y^2=6*x^6+2*x^5+32*x^4+28*x^3+7*x^2+6*x+21', 'y^2=14*x^6+7*x^5+34*x^4+29*x^3+19*x^2+20*x+17', 'y^2=12*x^6+38*x^5+31*x^4+26*x^3+16*x^2+7*x+1', 'y^2=2*x^6+17*x^5+x^4+8*x^3+38*x^2+16*x+24', 'y^2=30*x^6+27*x^5+34*x^4+39*x^3+8*x^2+8*x+2', 'y^2=27*x^6+29*x^5+30*x^4+8*x^3+15*x^2+17*x+11', 'y^2=8*x^6+22*x^5+x^4+34*x^3+33*x^2+5*x+39', 'y^2=24*x^6+14*x^5+37*x^4+7*x^3+31*x^2+20*x+30', 'y^2=11*x^6+35*x^5+33*x^4+7*x^3+24*x^2+12*x+1', 'y^2=13*x^5+35*x^4+35*x^3+16*x^2+4*x+11', 'y^2=16*x^6+23*x^5+18*x^4+11*x^3+16*x^2+15*x+11', 'y^2=16*x^6+4*x^5+2*x^4+34*x^3+24*x^2+23*x+25', 'y^2=23*x^6+22*x^5+40*x^4+17*x^3+38*x^2+28*x+35', 'y^2=38*x^6+3*x^5+16*x^4+36*x^3+38*x^2+16*x+38', 'y^2=18*x^6+28*x^5+21*x^4+17*x^3+36*x^2+33*x', 'y^2=8*x^6+17*x^4+18*x^3+9*x^2+32*x', 'y^2=38*x^6+37*x^5+14*x^4+x^3+18*x^2+7*x+4', 'y^2=36*x^6+29*x^5+17*x^4+40*x^3+4*x^2+32*x+27', 'y^2=24*x^6+31*x^5+25*x^4+22*x^3+28*x^2+9*x+6', 'y^2=x^6+16*x^5+28*x^4+2*x^3+21*x^2+19*x+6', 'y^2=17*x^6+15*x^5+19*x^4+11*x^3+24*x^2+21*x+16', 'y^2=17*x^6+24*x^5+23*x^4+23*x^3+5*x^2+33*x+22', 'y^2=21*x^6+19*x^5+x^4+37*x^3+3*x^2+7*x+35', 'y^2=5*x^6+11*x^5+35*x^4+7*x^3+22*x^2+10*x+7', 'y^2=4*x^6+6*x^5+31*x^4+14*x^3+x^2+34*x+20', 'y^2=32*x^6+40*x^5+4*x^4+35*x^3+5*x^2+19*x+40', 'y^2=17*x^6+15*x^5+25*x^4+37*x^3+34*x^2+32*x+15', 'y^2=18*x^6+7*x^4+25*x^3+13*x^2+2*x+30', 'y^2=15*x^6+29*x^5+15*x^4+21*x^3+20*x^2+19*x+11', 'y^2=30*x^6+19*x^5+39*x^4+23*x^3+3*x^2+12*x+23', 'y^2=x^6+17*x^5+36*x^4+2*x^3+26*x^2+20*x+21', 'y^2=3*x^6+x^5+40*x^4+15*x^3+32*x^2+39*x+21', 'y^2=25*x^6+37*x^5+5*x^4+7*x^3+27*x^2+25*x+35', 'y^2=8*x^6+37*x^5+19*x^4+29*x^3+38*x^2+3*x+33', 'y^2=2*x^6+4*x^5+34*x^4+22*x^3+31*x^2+27*x+35', 'y^2=16*x^6+40*x^5+37*x^4+29*x^3+39*x^2+13*x+19', 'y^2=37*x^6+7*x^5+6*x^4+32*x^3+14*x^2+20*x+1', 'y^2=3*x^6+34*x^5+11*x^4+31*x^3+5*x^2+20*x+1', 'y^2=17*x^6+31*x^5+16*x^4+29*x^3+22*x^2+24*x+11', 'y^2=10*x^6+10*x^5+18*x^4+4*x^2+35*x+39', 'y^2=9*x^6+24*x^5+26*x^4+31*x^3+33*x^2+8*x+11', 'y^2=32*x^6+14*x^5+39*x^4+25*x^3+5*x^2+2*x', 'y^2=29*x^6+11*x^5+2*x^4+2*x^3+15*x^2+24*x+39', 'y^2=27*x^6+40*x^5+38*x^4+39*x^3+8*x^2+6*x+1', 'y^2=x^6+7*x^5+x^4+7*x^3+11*x^2+9*x+10', 'y^2=8*x^6+16*x^5+34*x^4+39*x^3+7*x^2+35*x+28', 'y^2=32*x^6+10*x^5+21*x^4+18*x^3+20*x^2+11*x+32', 'y^2=17*x^6+35*x^5+21*x^4+24*x^3+23*x^2+38*x+2', 'y^2=30*x^6+29*x^5+14*x^4+35*x^3+29*x^2+19*x+34', 'y^2=19*x^6+35*x^5+35*x^4+26*x^3+8*x^2+19*x', 'y^2=34*x^6+11*x^5+34*x^4+8*x^3+20*x^2+11*x+9', 'y^2=21*x^6+2*x^5+15*x^4+4*x^3+8*x^2+32*x+17', 'y^2=9*x^6+22*x^4+28*x^3+37*x^2+24*x+19', 'y^2=28*x^6+19*x^5+15*x^4+27*x^3+31*x^2+15*x+27', 'y^2=15*x^6+17*x^5+40*x^4+21*x^3+14*x^2+35*x+16', 'y^2=20*x^6+23*x^5+10*x^4+15*x^3+30*x^2+18*x+40', 'y^2=36*x^6+21*x^5+23*x^4+5*x^3+38*x^2+33*x+1', 'y^2=39*x^6+39*x^5+11*x^4+15*x^3+9*x^2+35*x+39', 'y^2=5*x^6+7*x^5+25*x^4+21*x^3+31*x^2+4*x+12', 'y^2=9*x^6+18*x^5+20*x^4+38*x^3+10*x^2+25*x+30', 'y^2=26*x^6+16*x^5+14*x^4+11*x^3+2*x^2+2*x+26', 'y^2=2*x^6+30*x^5+26*x^4+20*x^3+12*x^2+26*x+29', 'y^2=2*x^6+6*x^5+40*x^4+29*x^3+26*x^2+5*x+15', 'y^2=2*x^6+26*x^5+40*x^4+8*x^3+33*x^2+15*x+38', 'y^2=9*x^6+18*x^5+18*x^4+23*x^3+28*x^2+24*x', 'y^2=5*x^6+5*x^5+21*x^4+28*x^3+39*x^2+9*x+27', 'y^2=19*x^6+18*x^5+15*x^4+35*x^3+10*x^2+6*x+17', 'y^2=15*x^6+9*x^5+34*x^4+34*x^3+37*x^2+18*x+10', 'y^2=14*x^6+15*x^5+3*x^4+4*x^3+17*x^2+2*x+33', 'y^2=8*x^6+25*x^5+6*x^4+6*x^3+5*x^2+29*x+10', 'y^2=26*x^6+9*x^5+26*x^4+24*x^3+5*x^2+31*x+36', 'y^2=14*x^6+22*x^5+31*x^4+22*x^3+8*x^2+34*x+39', 'y^2=36*x^6+10*x^5+5*x^4+11*x^3+7*x^2+10*x+24', 'y^2=27*x^6+20*x^5+4*x^4+4*x^3+12*x^2+32*x+4', 'y^2=29*x^6+32*x^5+38*x^4+24*x^3+x^2+32*x+25', 'y^2=32*x^6+27*x^5+19*x^4+31*x^3+2*x^2+14*x+18', 'y^2=16*x^6+17*x^5+12*x^4+39*x^3+5*x^2+26*x+17', 'y^2=12*x^6+32*x^5+3*x^4+3*x^3+19*x^2+37*x+6', 'y^2=35*x^6+28*x^5+23*x^4+34*x^3+20*x^2+18*x+18', 'y^2=26*x^6+11*x^5+27*x^4+15*x^3+12*x^2+13*x+34', 'y^2=15*x^6+22*x^5+40*x^4+28*x^3+7*x^2+19*x+11', 'y^2=20*x^6+5*x^5+x^4+8*x^2+20*x+8', 'y^2=16*x^6+8*x^5+5*x^4+37*x^3+21*x^2+22*x+34', 'y^2=11*x^6+4*x^5+37*x^4+4*x^3+12*x^2+35*x+40', 'y^2=39*x^6+28*x^5+2*x^4+18*x^3+22*x^2+29*x+14', 'y^2=17*x^6+x^5+11*x^3+25*x^2+37*x+3', 'y^2=32*x^6+36*x^5+31*x^3+34*x^2+7*x+24', 'y^2=9*x^6+19*x^5+37*x^4+31*x^3+16*x^2+30*x+28', 'y^2=40*x^6+19*x^5+10*x^4+17*x^3+19*x^2+23*x+34', 'y^2=9*x^6+29*x^5+38*x^4+12*x^3+24*x^2+2*x+14', 'y^2=19*x^6+33*x^5+5*x^4+11*x^3+27*x^2+15*x+19', 'y^2=22*x^6+27*x^5+11*x^4+26*x^3+25*x^2+33*x+7', 'y^2=23*x^6+7*x^5+33*x^3+25*x^2+13*x+24', 'y^2=11*x^6+38*x^5+28*x^4+34*x^3+11*x^2+12*x+25', 'y^2=13*x^6+34*x^5+22*x^4+19*x^3+23*x^2+9*x+21', 'y^2=20*x^6+25*x^5+9*x^4+18*x^3+14*x^2+8*x+13', 'y^2=38*x^6+40*x^5+36*x^4+8*x^3+11*x^2+38*x+38', 'y^2=14*x^6+37*x^5+3*x^4+7*x^3+23*x^2+13*x+25', 'y^2=18*x^6+19*x^5+21*x^4+40*x^3+27*x^2+24*x+19', 'y^2=7*x^6+15*x^5+17*x^4+30*x^3+11*x^2+12*x+7', 'y^2=37*x^6+7*x^5+17*x^4+35*x^3+28*x^2+8*x+4', 'y^2=8*x^6+39*x^5+32*x^4+17*x^3+15*x^2+37*x+35', 'y^2=30*x^6+20*x^5+24*x^4+23*x^3+27*x^2+32*x+37'], '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': 8, 'g': 2, 'galois_groups': ['4T3'], 'geom_dim1_distinct': 0, 'geom_dim1_factors': 0, 'geom_dim2_distinct': 1, 'geom_dim2_factors': 1, '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': 4, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['4T3'], 'geometric_number_fields': ['4.0.105472.1'], 'geometric_splitting_field': '4.0.105472.1', 'geometric_splitting_polynomials': [[103, 0, 22, 0, 1]], 'group_structure_count': 3, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 126, 'is_cyclic': False, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 126, 'label': '2.41.ae_o', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['4.0.105472.1'], 'p': 41, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 7, 1, 12], [1, 23, 1, 6], [1, 41, 1, 12], [1, 71, 2, 6]], 'poly': [1, -4, 14, -164, 1681], 'poly_str': '1 -4 14 -164 1681 ', 'primitive_models': [], 'principal_polarization_count': 126, 'q': 41, 'real_poly': [1, -4, -68], 'simple_distinct': ['2.41.ae_o'], 'simple_factors': ['2.41.ae_oA'], 'simple_multiplicities': [1], 'singular_primes': ['2,3*V-17', '3,8*F^2+V-4'], 'size': 294, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.105472.1', 'splitting_polynomials': [[103, 0, 22, 0, 1]], 'twist_count': 2, 'twists': [['2.41.e_o', '2.1681.m_dik', 2]], 'weak_equivalence_count': 10, 'zfv_index': 72, 'zfv_index_factorization': [[2, 3], [3, 2]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_pic_size': 96, 'zfv_plus_index': 6, 'zfv_plus_index_factorization': [[2, 1], [3, 1]], 'zfv_plus_norm': 6592, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,3*V-17', '3,8*F^2+V-4']}
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av_fq_endalg_factors • Show schema
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{'base_label': '2.41.ae_o', 'extension_degree': 1, 'extension_label': '2.41.ae_o', 'multiplicity': 1}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0', '0', '0', '0'], 'center': '4.0.105472.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.41.ae_o', 'galois_group': '4T3', 'places': [['26', '1', '0', '0'], ['9', '1', '0', '0'], ['15', '1', '0', '0'], ['32', '1', '0', '0']]}
