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av_fq_isog • Show schema
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{'abvar_count': 1667, 'abvar_counts': [1667, 2778889, 4750176512, 8002669552201, 13422659125827827, 22564176895156486144, 37929227195289567246467, 63758964013038451340015625, 107178930967531131949058861312, 180167778008169044896628047541929], 'abvar_counts_str': '1667 2778889 4750176512 8002669552201 13422659125827827 22564176895156486144 37929227195289567246467 63758964013038451340015625 107178930967531131949058861312 180167778008169044896628047541929 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.220721427874418, 0.779278572125582], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 42, 'curve_counts': [42, 1652, 68922, 2832036, 115856202, 4750248782, 194754273882, 7984916850628, 327381934393962, 13422658941503252], 'curve_counts_str': '42 1652 68922 2832036 115856202 4750248782 194754273882 7984916850628 327381934393962 13422658941503252 ', 'curves': ['y^2=7*x^6+29*x^5+6*x^4+36*x^3+17*x^2+25*x+34', 'y^2=x^6+10*x^5+36*x^4+11*x^3+20*x^2+27*x+40', 'y^2=19*x^6+25*x^5+31*x^4+26*x^3+20*x^2+20*x+31', 'y^2=33*x^6+5*x^5+16*x^4+x^3+4*x^2+40*x+16', 'y^2=3*x^6+8*x^5+22*x^4+30*x^3+32*x^2+30*x+21', 'y^2=18*x^6+7*x^5+9*x^4+16*x^3+28*x^2+16*x+3', 'y^2=5*x^6+3*x^5+14*x^4+30*x^3+4*x^2+36*x+21', 'y^2=4*x^6+17*x^5+17*x^4+x^3+4*x^2+5*x+38', 'y^2=24*x^6+20*x^5+20*x^4+6*x^3+24*x^2+30*x+23', 'y^2=25*x^6+38*x^5+36*x^4+31*x^3+x^2+10*x+30', 'y^2=23*x^6+10*x^5+36*x^4+16*x^3+12*x^2+23*x+24', 'y^2=15*x^6+19*x^5+11*x^4+14*x^3+31*x^2+15*x+21', 'y^2=26*x^6+30*x^5+20*x^4+35*x^3+23*x^2+23*x+40', 'y^2=2*x^6+x^5+35*x^4+19*x^2+14*x+19', 'y^2=12*x^6+6*x^5+5*x^4+32*x^2+2*x+32', 'y^2=31*x^6+17*x^5+9*x^4+9*x^3+x^2+15*x+28', 'y^2=22*x^6+20*x^5+13*x^4+13*x^3+6*x^2+8*x+4', 'y^2=19*x^6+10*x^5+39*x^4+12*x^3+31*x^2+32*x+13', 'y^2=32*x^6+19*x^5+29*x^4+31*x^3+22*x^2+28*x+37', 'y^2=x^6+6*x^5+38*x^4+40*x^3+39*x^2+10*x+1', 'y^2=29*x^6+35*x^5+28*x^4+4*x^3+30*x^2+28*x+1'], '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': 2, 'g': 2, 'galois_groups': ['4T2'], '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': ['2.0.6499.1'], 'geometric_splitting_field': '2.0.6499.1', 'geometric_splitting_polynomials': [[1625, -1, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 21, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 21, 'label': '2.41.a_ap', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 4, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['4.0.42237001.1'], 'p': 41, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 5, 1, 7], [1, 47, 1, 21]], 'poly': [1, 0, -15, 0, 1681], 'poly_str': '1 0 -15 0 1681 ', 'primitive_models': [], 'principal_polarization_count': 28, 'q': 41, 'real_poly': [1, 0, -97], 'simple_distinct': ['2.41.a_ap'], 'simple_factors': ['2.41.a_apA'], 'simple_multiplicities': [1], 'singular_primes': ['2,F^2+4*F-5*V-4'], 'size': 28, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.42237001.1', 'splitting_polynomials': [[1681, 0, -15, 0, 1]], 'twist_count': 2, 'twists': [['2.41.a_p', '2.2825761.jhi_bhxlpj', 4]], 'weak_equivalence_count': 2, 'zfv_index': 4, 'zfv_index_factorization': [[2, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_pic_size': 21, 'zfv_plus_index': 2, 'zfv_plus_index_factorization': [[2, 1]], 'zfv_plus_norm': 4489, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,F^2+4*F-5*V-4']}
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av_fq_endalg_factors • Show schema
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id: 27971
{'base_label': '2.41.a_ap', 'extension_degree': 1, 'extension_label': '2.41.a_ap', 'multiplicity': 1}
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id: 27972
{'base_label': '2.41.a_ap', 'extension_degree': 2, 'extension_label': '1.1681.ap', 'multiplicity': 2}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0', '0'], 'center': '4.0.42237001.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.41.a_ap', 'galois_group': '4T2', 'places': [['0', '15/41', '0', '1680/41'], ['0', '1', '0', '0']]}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0', '0'], 'center': '2.0.6499.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.1681.ap', 'galois_group': '2T1', 'places': [['33', '1'], ['7', '1']]}
