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av_fq_isog • Show schema
{'abvar_count': 80, 'abvar_counts': [80, 6400, 527360, 64000000, 3512856400, 278108569600, 22858581253840, 1964262400000000, 150085819531627520, 12340160087020960000], 'abvar_counts_str': '80 6400 527360 64000000 3512856400 278108569600 22858581253840 1964262400000000 150085819531627520 12340160087020960000 ', 'angle_corank': 2, 'angle_rank': 2, 'angles': [0.144188681099749, 0.32433441433903, 0.67566558566097, 0.855811318900252], 'center_dim': 8, 'cohen_macaulay_max': 3, 'curve_count': 4, 'curve_counts': [4, 8, 28, 112, 244, 722, 2188, 6944, 19684, 59928], 'curve_counts_str': '4 8 28 112 244 722 2188 6944 19684 59928 ', 'curves': ['y^2=x^9+2*x^7+2*x^5+2*x^3+2*x', 'y^2=x^10+x^9+2*x^8+2*x^6+x^4+x^2+x+2', 'y^2=x^10+x^9+2*x^8+x^6+x^4+2*x^2+x', 'y^2=x^9+x^7+2*x^5+x^3+2*x', 'y^2=x^9+x^8+x^5+2*x^3+2*x^2+2*x', 'x*y+t^2=y^2*z+y*z^2-z^3+x^2*t+x*z*t+y*z*t+z^2*t=0', 'x*y+t^2=y^2*z-y*z^2+z^3+x^2*t+x*z*t-z^2*t=0', 'x*y+t^2=y^3+x*z^2-y*z^2+z^3+x^2*t+y^2*t+y*z*t+z^2*t=0', 'x*y+t^2=y^2*z+x*z^2+y*z^2+z^3+x^2*t-x*y*t+x*z*t+y*z*t+z^2*t=0', 'x*y+t^2=y^3+x*y*z+y^2*z+x*z^2-y*z^2-z^3+x^2*t-y^2*t-x*z*t+y*z*t+z^2*t=0', 'x*y+t^2=x^2*z-x*y*z+y^2*z+y*z^2-z^3+y^2*t+y*z*t=0', 'x^2+y^2+z*t=y^2*z+y*z^2+y*z*t+z^2*t+x*t^2-y*t^2=0', 'x^2+y^2+z*t=y^3-y*z^2-z^3+y^2*t+x*z*t+z^2*t-y*t^2-z*t^2=0', 'x^2+y^2+z*t=y^3-y*z^2-z^3+y^2*t+x*z*t+y*z*t+z^2*t-x*t^2=0', 'x^2+y^2+z*t=y^3+y^2*z+y*z^2+x*z*t+z^2*t-x*t^2-z*t^2+t^3=0'], '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': 24, 'g': 4, 'galois_groups': ['8T18'], 'geom_dim1_distinct': 0, 'geom_dim1_factors': 0, 'geom_dim2_distinct': 1, 'geom_dim2_factors': 2, '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': 2, 'geometric_galois_groups': ['4T3'], 'geometric_number_fields': ['4.0.67240.1'], 'geometric_splitting_field': '4.0.65600.5', 'geometric_splitting_polynomials': [[25, -10, 1, -2, 1]], 'group_structure_count': 5, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 5, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 15, 'label': '4.3.a_ab_a_i', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 4, 'newton_coelevation': 6, 'newton_elevation': 0, 'number_fields': ['8.0.4521217600.1'], 'p': 3, 'p_rank': 4, 'p_rank_deficit': 0, 'poly': [1, 0, -1, 0, 8, 0, -9, 0, 81], 'poly_str': '1 0 -1 0 8 0 -9 0 81 ', 'primitive_models': [], 'q': 3, 'real_poly': [1, 0, -13, 0, 32], 'simple_distinct': ['4.3.a_ab_a_i'], 'simple_factors': ['4.3.a_ab_a_iA'], 'simple_multiplicities': [1], 'singular_primes': ['2,10*F^3+16*F+11*V^3-3*V^2+23*V+2', '2,-6*F^3-2*F^2+9*F-2*V^2-26*V-1'], 'slopes': ['0A', '0B', '0C', '0D', '1A', '1B', '1C', '1D'], 'splitting_field': '8.0.4521217600.1', 'splitting_polynomials': [[16, 0, 4, 0, -2, 0, 1, 0, 1], [20, -30, 41, 15, -13, 6, 3, -3, 1]], 'twist_count': 2, 'twists': [['4.3.a_b_a_i', '4.81.be_yr_mvm_fhiq', 4]], 'weak_equivalence_count': 30, 'zfv_index': 256, 'zfv_index_factorization': [[2, 8]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 8, 'zfv_plus_index_factorization': [[2, 3]], 'zfv_plus_norm': 400, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,10*F^3+16*F+11*V^3-3*V^2+23*V+2', '2,-6*F^3-2*F^2+9*F-2*V^2-26*V-1']} - av_fq_endalg_factors • Show schema
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av_fq_endalg_data • Show schema
{'brauer_invariants': ['0', '0'], 'center': '8.0.4521217600.1', 'center_dim': 8, 'divalg_dim': 1, 'extension_label': '4.3.a_ab_a_i', 'galois_group': '8T18', 'places': [['2', '1', '2', '1', '2', '0', '0', '0'], ['2', '2', '2', '2', '2', '0', '0', '0']]} -
av_fq_endalg_data • Show schema
{'brauer_invariants': ['0', '0'], 'center': '4.0.67240.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.9.ab_i', 'galois_group': '4T3', 'places': [['0', '2', '2', '1'], ['2', '0', '2', '1']]}
Abelian variety isogeny class data - 4.3.a_ab_a_i