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av_fq_isog • Show schema
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{'abvar_count': 279, 'abvar_counts': [279, 22599, 2101707, 248430807, 29957095179, 3819635996679, 469599929948736, 59969746222317927, 7465530020296348359, 930757275293737603239], 'abvar_counts_str': '279 22599 2101707 248430807 29957095179 3819635996679 469599929948736 59969746222317927 7465530020296348359 930757275293737603239 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 0, 'angle_rank': 3, 'angles': [0.348097716608178, 0.579933069652494, 0.843561104768793], 'center_dim': 6, 'cohen_macaulay_max': 1, 'curve_count': 9, 'curve_counts': [9, 35, 135, 635, 3069, 15647, 76932, 393011, 1957041, 9759695], 'curve_counts_str': '9 35 135 635 3069 15647 76932 393011 1957041 9759695 ', 'curves': ['y^2=x^7+x^4+x^2+x+4', 'y^2=x^7+2*x^4+x^3+x^2+4*x+4', 'y^2=x^7+2*x^4+3*x^3+x^2+2*x+4', 'y^2=x^7+3*x^5+2*x^4+2*x^2+2*x+1', 'y^2=x^7+3*x^5+2*x^4+3*x^3+x^2+4*x+4', 'y^2=x^7+4*x^5+2*x^4+x^3+3*x^2+x+1', '2*x^3*y+4*x^3*z+2*x^2*y^2+x^2*z^2+x*z^3+y^3*z=0', '4*x^3*y+3*x^3*z+4*x^2*y^2+x^2*y*z+x^2*z^2+x*z^3+y^3*z=0', '4*x^4+x^3*y+2*x^3*z+3*x^2*y*z+x^2*z^2+x*z^3+y^3*z=0', '2*x^4+2*x^3*y+x^3*z+x^2*y^2+3*x^2*y*z+x^2*z^2+x*z^3+y^3*z=0', 'x^4+2*x^3*z+x^2*y^2+3*x^2*y*z+x^2*z^2+x*z^3+y^3*z=0', '2*x^4+2*x^3*y+3*x^3*z+x^2*y^2+4*x^2*y*z+x^2*z^2+x*z^3+y^3*z=0', '2*x^4+4*x^3*y+2*x^3*z+3*x^2*y^2+4*x^2*y*z+x^2*z^2+x*z^3+y^3*z=0', '2*x^4+3*x^3*z+2*x^2*y^2+x*y*z^2+x*z^3+y^3*z=0', 'x^3*y+4*x^3*z+4*x^2*y^2+x*y*z^2+x*z^3+y^3*z=0', '3*x^4+4*x^3*y+x^3*z+x^2*y^2+x^2*y*z+x*y*z^2+x*z^3+y^3*z=0', 'x^4+4*x^3*y+4*x^3*z+3*x^2*y^2+3*x^2*y*z+x*y*z^2+x*z^3+y^3*z=0', 'x^4+x^3*y+x^2*z^2+x*y*z^2+x*z^3+y^3*z=0', '4*x^4+x^3*z+x^2*y^2+x^2*y*z+x^2*z^2+x*y*z^2+x*z^3+y^3*z=0', 'x^4+x^3*y+4*x^3*z+3*x^2*y^2+x^2*y*z+x^2*z^2+x*y*z^2+x*z^3+y^3*z=0', '3*x^4+x^3*y+3*x^3*z+2*x^2*y^2+2*x^2*y*z+x^2*z^2+x*y*z^2+x*z^3+y^3*z=0', 'x^4+3*x^3*y+2*x^3*z+3*x^2*y^2+3*x^2*y*z+x^2*z^2+x*y*z^2+x*z^3+y^3*z=0', '4*x^4+x^3*y+4*x^3*z+x^2*y^2+x*z^3+y^4+y^2*z^2=0', 'x^4+3*x^3*y+x^3*z+x^2*y^2+x^2*y*z+x*z^3+y^4+y^2*z^2=0', '4*x^4+x^3*y+4*x^3*z+2*x^2*y^2+2*x^2*y*z+x*z^3+y^4+y^2*z^2=0', '2*x^4+4*x^3*y+2*x^3*z+3*x^2*y^2+2*x^2*y*z+x*z^3+y^4+y^2*z^2=0', '2*x^4+3*x^3*y+3*x^3*z+x^2*y^2+2*x^2*y*z+x^2*z^2+x*z^3+y^4+y^2*z^2=0', '4*x^4+4*x^3*y+x^3*z+x^2*y^2+2*x^2*y*z+3*x^2*z^2+x*z^3+y^4+y^2*z^2=0', '4*x^4+x^3*y+x^3*z+4*x^2*y^2+2*x^2*y*z+4*x^2*z^2+x*z^3+y^4+y^2*z^2=0', '4*x^4+3*x^3*y+3*x^3*z+x^2*y^2+x^2*y*z+x*y^3+x*z^3+y^4+y^2*z^2=0'], 'dim1_distinct': 0, 'dim1_factors': 0, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 1, 'dim3_factors': 1, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'endomorphism_ring_count': 4, 'g': 3, 'galois_groups': ['6T11'], 'geom_dim1_distinct': 0, 'geom_dim1_factors': 0, 'geom_dim2_distinct': 0, 'geom_dim2_factors': 0, 'geom_dim3_distinct': 1, 'geom_dim3_factors': 1, 'geom_dim4_distinct': 0, 'geom_dim4_factors': 0, 'geom_dim5_distinct': 0, 'geom_dim5_factors': 0, 'geometric_center_dim': 6, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['6T11'], 'geometric_number_fields': ['6.0.135911079.1'], 'geometric_splitting_field': '6.0.135911079.1', 'geometric_splitting_polynomials': [[81, 21, 21, -5, 9, -3, 1]], 'group_structure_count': 2, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 6, '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': 30, 'label': '3.5.d_j_v', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 4, 'newton_elevation': 0, 'noncyclic_primes': [3], 'number_fields': ['6.0.135911079.1'], 'p': 5, 'p_rank': 3, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 2, 1, 13], [1, 31, 1, 26]], 'poly': [1, 3, 9, 21, 45, 75, 125], 'poly_str': '1 3 9 21 45 75 125 ', 'primitive_models': [], 'principal_polarization_count': 39, 'q': 5, 'real_poly': [1, 3, -6, -9], 'simple_distinct': ['3.5.d_j_v'], 'simple_factors': ['3.5.d_j_vA'], 'simple_multiplicities': [1], 'singular_primes': ['3,-F^3+3*F^2-4*F-V-4', '3,F^3-3*F^2+5*F+V^2+V+3'], 'size': 65, 'slopes': ['0A', '0B', '0C', '1A', '1B', '1C'], 'splitting_field': '6.0.135911079.1', 'splitting_polynomials': [[81, 21, 21, -5, 9, -3, 1]], 'twist_count': 2, 'twists': [['3.5.ad_j_av', '3.25.j_bt_gn', 2]], 'weak_equivalence_count': 4, 'zfv_index': 9, 'zfv_index_factorization': [[3, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_pic_size': 26, 'zfv_plus_index': 3, 'zfv_plus_index_factorization': [[3, 1]], 'zfv_plus_norm': 1319, 'zfv_singular_count': 4, 'zfv_singular_primes': ['3,-F^3+3*F^2-4*F-V-4', '3,F^3-3*F^2+5*F+V^2+V+3']}
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av_fq_endalg_factors • Show schema
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{'base_label': '3.5.d_j_v', 'extension_degree': 1, 'extension_label': '3.5.d_j_v', 'multiplicity': 1}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0', '0'], 'center': '6.0.135911079.1', 'center_dim': 6, 'divalg_dim': 1, 'extension_label': '3.5.d_j_v', 'galois_group': '6T11', 'places': [['23/5', '11/5', '4/5', '4/5', '21/5', '2/5'], ['17/5', '14/5', '21/5', '21/5', '4/5', '23/5']]}
