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av_fq_isog • Show schema
{'abvar_count': 11, 'abvar_counts': [11, 253, 1727, 74129, 537581, 13862629, 272117857, 5535434817, 65832284969, 1017475795633], 'abvar_counts_str': '11 253 1727 74129 537581 13862629 272117857 5535434817 65832284969 1017475795633 ', 'angle_corank': 0, 'angle_rank': 4, 'angles': [0.0640918585256743, 0.393625989811032, 0.651207033805291, 0.823657974581194], 'center_dim': 8, 'cohen_macaulay_max': 2, 'curve_count': 3, 'curve_counts': [3, 5, 3, 17, 13, 53, 129, 321, 489, 945], 'curve_counts_str': '3 5 3 17 13 53 129 321 489 945 ', 'curves': ['y^2 + y=x^9 + x^7 + x^3 + 1'], 'dim1_distinct': 0, 'dim1_factors': 0, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 0, 'dim3_factors': 0, 'dim4_distinct': 1, 'dim4_factors': 1, 'dim5_distinct': 0, 'dim5_factors': 0, 'endomorphism_ring_count': 6, 'g': 4, 'galois_groups': ['8T44'], 'geom_dim1_distinct': 0, 'geom_dim1_factors': 0, 'geom_dim2_distinct': 0, 'geom_dim2_factors': 0, 'geom_dim3_distinct': 0, 'geom_dim3_factors': 0, 'geom_dim4_distinct': 1, 'geom_dim4_factors': 1, 'geom_dim5_distinct': 0, 'geom_dim5_factors': 0, 'geometric_center_dim': 8, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['8T44'], 'geometric_number_fields': ['8.0.5198736512.1'], 'geometric_splitting_field': '8.0.5198736512.1', 'geometric_splitting_polynomials': [[16, -24, 12, -2, 0, -1, 3, -3, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 1, 'is_cyclic': True, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 1, 'label': '4.2.a_a_ac_a', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 1, 'newton_elevation': 5, 'noncyclic_primes': [], 'number_fields': ['8.0.5198736512.1'], 'p': 2, 'p_rank': 0, 'p_rank_deficit': 4, 'poly': [1, 0, 0, -2, 0, -4, 0, 0, 16], 'poly_str': '1 0 0 -2 0 -4 0 0 16 ', 'primitive_models': [], 'q': 2, 'real_poly': [1, 0, -8, -2, 8], 'simple_distinct': ['4.2.a_a_ac_a'], 'simple_factors': ['4.2.a_a_ac_aA'], 'simple_multiplicities': [1], 'singular_primes': ['2,-2*F^3-F+4*V^2+2*V-4,2*F^4-2*F^2-V^3-3*V-2'], 'slopes': ['1/3A', '1/3B', '1/3C', '1/2A', '1/2B', '2/3A', '2/3B', '2/3C'], 'splitting_field': '8.0.5198736512.1', 'splitting_polynomials': [[16, -24, 12, -2, 0, -1, 3, -3, 1]], 'twist_count': 2, 'twists': [['4.2.a_a_c_a', '4.4.a_a_ae_q', 2]], 'weak_equivalence_count': 7, 'zfv_index': 8, 'zfv_index_factorization': [[2, 3]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 2, 'zfv_plus_index_factorization': [[2, 1]], 'zfv_plus_norm': 32, 'zfv_singular_count': 3, 'zfv_singular_primes': ['2,-2*F^3-F+4*V^2+2*V-4,2*F^4-2*F^2-V^3-3*V-2']} -
av_fq_endalg_factors • Show schema
{'base_label': '4.2.a_a_ac_a', 'extension_degree': 1, 'extension_label': '4.2.a_a_ac_a', 'multiplicity': 1} -
av_fq_endalg_data • Show schema
{'brauer_invariants': ['0', '0', '0'], 'center': '8.0.5198736512.1', 'center_dim': 8, 'divalg_dim': 1, 'extension_label': '4.2.a_a_ac_a', 'galois_group': '8T44', 'places': [['0', '3/2', '7/4', '0', '15/8', '11/8', '13/8', '9/8'], ['1', '3/2', '3/4', '0', '15/8', '3/8', '13/8', '1/8'], ['1', '1', '0', '0', '0', '0', '0', '0']]}
Abelian variety isogeny class data - 4.2.a_a_ac_a