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av_fq_isog • Show schema
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{'abvar_count': 375, 'abvar_counts': [375, 140625, 47034000, 17128265625, 6131071134375, 2212197156000000, 799006684634613375, 288439879410444515625, 104127350297910715386000, 37590033254766349306640625], 'abvar_counts_str': '375 140625 47034000 17128265625 6131071134375 2212197156000000 799006684634613375 288439879410444515625 104127350297910715386000 37590033254766349306640625 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.30556997246711, 0.69443002753289], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 20, 'curve_counts': [20, 388, 6860, 131428, 2476100, 47022118, 893871740, 16983472708, 322687697780, 6131076010948], 'curve_counts_str': '20 388 6860 131428 2476100 47022118 893871740 16983472708 322687697780 6131076010948 ', 'curves': ['y^2=x^6+9*x^5+17*x^4+13*x^3+11*x^2+16*x+8', 'y^2=2*x^6+18*x^5+15*x^4+7*x^3+3*x^2+13*x+16', 'y^2=3*x^6+13*x^5+4*x^4+15*x^3+5*x^2+12*x+2', 'y^2=6*x^6+7*x^5+8*x^4+11*x^3+10*x^2+5*x+4', 'y^2=4*x^6+14*x^5+8*x^4+10*x^3+9*x^2+16*x+9', 'y^2=8*x^6+9*x^5+16*x^4+x^3+18*x^2+13*x+18', 'y^2=5*x^6+17*x^5+8*x^4+3*x^3+17*x^2+7*x+2', 'y^2=11*x^6+18*x^5+10*x^4+3*x^3+6*x^2+12*x+7', 'y^2=3*x^6+17*x^5+x^4+6*x^3+12*x^2+5*x+14', 'y^2=9*x^6+7*x^5+15*x^4+10*x^3+16*x^2+14*x+16', 'y^2=18*x^6+14*x^5+11*x^4+x^3+13*x^2+9*x+13', 'y^2=12*x^6+4*x^5+6*x^4+5*x^3+4*x^2+11*x+1', 'y^2=5*x^6+8*x^5+12*x^4+10*x^3+8*x^2+3*x+2', 'y^2=8*x^6+16*x^5+10*x^4+6*x^3+7*x^2+x+7', 'y^2=5*x^6+17*x^5+9*x^4+2*x^3+14*x^2+9*x+3', 'y^2=13*x^6+15*x^5+5*x^4+18*x^3+x^2+x+13', 'y^2=7*x^6+11*x^5+10*x^4+17*x^3+2*x^2+2*x+7', 'y^2=10*x^6+6*x^5+11*x^4+14*x^3+7*x^2+4*x+10', 'y^2=x^6+12*x^5+3*x^4+9*x^3+14*x^2+8*x+1', 'y^2=7*x^6+6*x^5+x^3+5*x+18', 'y^2=10*x^6+11*x^5+7*x^4+11*x^3+11*x^2+7*x+10', 'y^2=x^6+3*x^5+14*x^4+3*x^3+3*x^2+14*x+1', 'y^2=7*x^6+11*x^5+8*x^4+9*x^3+5*x^2+6*x+5', 'y^2=14*x^6+3*x^5+16*x^4+18*x^3+10*x^2+12*x+10', 'y^2=6*x^6+10*x^5+13*x^4+6*x^3+5*x^2+18*x+8', 'y^2=12*x^6+x^5+7*x^4+12*x^3+10*x^2+17*x+16', 'y^2=6*x^6+x^5+8*x^4+15*x^3+x^2+3*x+9', 'y^2=12*x^6+2*x^5+16*x^4+11*x^3+2*x^2+6*x+18', 'y^2=8*x^6+3*x^5+11*x^4+8*x^3+15*x^2+12*x+12', 'y^2=16*x^6+6*x^5+3*x^4+16*x^3+11*x^2+5*x+5', 'y^2=12*x^6+16*x^5+17*x^4+10*x^3+15*x^2+15*x+1', 'y^2=5*x^6+13*x^5+15*x^4+x^3+11*x^2+11*x+2', 'y^2=2*x^6+4*x^5+7*x^4+18*x^3+4*x^2+17*x+13', 'y^2=4*x^6+8*x^5+14*x^4+17*x^3+8*x^2+15*x+7', 'y^2=11*x^6+7*x^5+12*x^4+3*x^3+8*x^2+6', 'y^2=3*x^6+14*x^5+5*x^4+6*x^3+16*x^2+12', 'y^2=4*x^6+18*x^5+5*x^4+17*x^3+16*x^2+8*x+4', 'y^2=8*x^6+17*x^5+10*x^4+15*x^3+13*x^2+16*x+8'], 'dim1_distinct': 2, '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, 'endomorphism_ring_count': 8, 'g': 2, 'galois_groups': ['2T1', '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': 2, 'geometric_galois_groups': ['2T1'], 'geometric_number_fields': ['2.0.51.1'], 'geometric_splitting_field': '2.0.51.1', 'geometric_splitting_polynomials': [[13, -1, 1]], 'group_structure_count': 2, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 38, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 38, 'label': '2.19.a_n', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 6, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [5], 'number_fields': ['2.0.51.1', '2.0.51.1'], 'p': 19, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 3, 1, 4], [2, 3, 1, 4], [1, 11, 1, 12]], 'poly': [1, 0, 13, 0, 361], 'poly_str': '1 0 13 0 361 ', 'primitive_models': [], 'principal_polarization_count': 48, 'q': 19, 'real_poly': [1, 0, -25], 'simple_distinct': ['1.19.af', '1.19.f'], 'simple_factors': ['1.19.afA', '1.19.fA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['2,-F^2+7*V-8', '5,2*F+2', '5,-V-1'], 'size': 208, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '2.0.51.1', 'splitting_polynomials': [[13, -1, 1]], 'twist_count': 6, 'twists': [['2.19.ak_cl', '2.361.ba_bih', 2], ['2.19.k_cl', '2.361.ba_bih', 2], ['2.19.a_an', '2.130321.bqo_bgfyp', 4], ['2.19.af_g', '2.47045881.abjea_tuwbzy', 6], ['2.19.f_g', '2.47045881.abjea_tuwbzy', 6]], 'weak_equivalence_count': 8, 'zfv_index': 100, 'zfv_index_factorization': [[2, 2], [5, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_pic_size': 96, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 2601, 'zfv_singular_count': 6, 'zfv_singular_primes': ['2,-F^2+7*V-8', '5,2*F+2', '5,-V-1']}
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av_fq_endalg_factors • Show schema
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id: 12468
{'base_label': '2.19.a_n', 'extension_degree': 1, 'extension_label': '1.19.af', 'multiplicity': 1}
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id: 12469
{'base_label': '2.19.a_n', 'extension_degree': 1, 'extension_label': '1.19.f', 'multiplicity': 1}
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id: 12470
{'base_label': '2.19.a_n', 'extension_degree': 2, 'extension_label': '1.361.n', 'multiplicity': 2}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0', '0'], 'center': '2.0.51.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.19.af', 'galois_group': '2T1', 'places': [['16', '1'], ['2', '1']]}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0', '0'], 'center': '2.0.51.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.19.f', 'galois_group': '2T1', 'places': [['2', '1'], ['16', '1']]}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0', '0'], 'center': '2.0.51.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.361.n', 'galois_group': '2T1', 'places': [['16', '1'], ['2', '1']]}
