-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [445, -1802, 5265, -7020, 4680, -4212, 2990, -1300, 806, -364, 104, -52, 13, -2, 1], 'conductor': 0, 'degree': 14, 'disc_abs': 20325604337285010030592, 'disc_rad': 26, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [4732, 2338], 'galois_label': '14T39', 'galt': 39, 'grd': 69.93946361168216, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '14.2.20325604337285010030592.1', 'local_algs': ['2.1.6.10a1.5', '2.2.4.16a1.1', '13.1.1.0a1.1', '13.1.13.13a1.10'], 'maxp': 13, 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 6, 'ramps': [2, 13], 'rd': 39.2131450854, 'regulator': {'__RealLiteral__': 0, 'data': '1523520.8954', 'prec': 40}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 2, 'used_grh': True} -
nf_fields_extra • Show schema
{'dirichlet_group': [], 'frobs': [[2, [0]], [3, [[7, 2]]], [5, [[12, 1], [1, 2]]], [7, [[12, 1], [1, 2]]], [11, [[12, 1], [1, 2]]], [13, [0]], [17, [[3, 4], [1, 2]]], [19, [[14, 1]]], [23, [[7, 2]]], [29, [[7, 2]]], [31, [[2, 7]]], [37, [[4, 3], [1, 2]]], [41, [[14, 1]]], [43, [[7, 2]]], [47, [[14, 1]]], [53, [[7, 2]]], [59, [[4, 3], [1, 2]]]], 'label': '14.2.20325604337285010030592.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{1}{160} a^{13} - \\frac{1}{80} a^{12} + \\frac{7}{160} a^{11} - \\frac{31}{160} a^{10} + \\frac{11}{80} a^{9} - \\frac{21}{160} a^{8} + \\frac{53}{160} a^{7} + \\frac{119}{40} a^{6} - \\frac{1031}{160} a^{5} + \\frac{259}{32} a^{4} - \\frac{1599}{80} a^{3} + \\frac{3517}{160} a^{2} - \\frac{107}{16} a + \\frac{27}{16} \\)', '\\( \\frac{1}{80} a^{13} - \\frac{7}{160} a^{12} + \\frac{33}{160} a^{11} - \\frac{131}{160} a^{10} + \\frac{41}{20} a^{9} - \\frac{911}{160} a^{8} + \\frac{2047}{160} a^{7} - \\frac{917}{40} a^{6} + \\frac{6783}{160} a^{5} - \\frac{9477}{160} a^{4} + \\frac{1371}{20} a^{3} - \\frac{2517}{32} a^{2} + \\frac{7807}{160} a - \\frac{321}{32} \\)', '\\( \\frac{1}{80} a^{13} - \\frac{1}{80} a^{12} + \\frac{11}{80} a^{11} - \\frac{41}{80} a^{10} + \\frac{29}{40} a^{9} - \\frac{57}{16} a^{8} + \\frac{551}{80} a^{7} - \\frac{361}{40} a^{6} + \\frac{2277}{80} a^{5} - \\frac{2631}{80} a^{4} + \\frac{1211}{40} a^{3} - \\frac{1103}{16} a^{2} + \\frac{181}{5} a + \\frac{87}{16} \\)', '\\( \\frac{1}{160} a^{13} - \\frac{3}{160} a^{12} + \\frac{3}{40} a^{11} - \\frac{7}{20} a^{10} + \\frac{27}{40} a^{9} - \\frac{37}{20} a^{8} + \\frac{73}{16} a^{7} - \\frac{91}{16} a^{6} + \\frac{447}{40} a^{5} - \\frac{157}{10} a^{4} + \\frac{73}{8} a^{3} - \\frac{117}{10} a^{2} + \\frac{541}{160} a - \\frac{35}{32} \\)', '\\( \\frac{1}{40} a^{13} + \\frac{13}{40} a^{11} - \\frac{51}{80} a^{10} + \\frac{21}{16} a^{9} - \\frac{51}{8} a^{8} + \\frac{563}{80} a^{7} - \\frac{1441}{80} a^{6} + \\frac{1481}{40} a^{5} - \\frac{2257}{80} a^{4} + \\frac{923}{16} a^{3} - \\frac{423}{8} a^{2} + \\frac{299}{16} a - \\frac{83}{16} \\)', '\\( \\frac{1}{40} a^{13} + \\frac{1}{160} a^{12} + \\frac{13}{40} a^{11} - \\frac{99}{160} a^{10} + \\frac{183}{160} a^{9} - \\frac{539}{80} a^{8} + \\frac{1053}{160} a^{7} - \\frac{2937}{160} a^{6} + \\frac{1667}{40} a^{5} - \\frac{4389}{160} a^{4} + \\frac{10841}{160} a^{3} - \\frac{5277}{80} a^{2} + \\frac{3743}{160} a - 7 \\)', '\\( \\frac{1}{40} a^{13} - \\frac{1}{16} a^{12} + \\frac{13}{40} a^{11} - \\frac{117}{80} a^{10} + \\frac{233}{80} a^{9} - \\frac{193}{20} a^{8} + \\frac{1857}{80} a^{7} - \\frac{2813}{80} a^{6} + \\frac{3259}{40} a^{5} - \\frac{9679}{80} a^{4} + \\frac{9739}{80} a^{3} - \\frac{3837}{20} a^{2} + \\frac{2349}{16} a - \\frac{257}{8} \\)'], 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2', '1/2*a^4 - 1/2*a', '1/2*a^5 - 1/2*a^2', '1/4*a^6 - 1/4', '1/8*a^7 - 1/8*a^6 - 1/4*a^4 - 1/4*a^3 - 1/2*a^2 - 3/8*a + 3/8', '1/40*a^8 - 3/40*a^6 + 1/20*a^5 + 1/5*a^4 - 1/20*a^3 - 19/40*a^2 + 1/10*a - 3/8', '1/40*a^9 + 1/20*a^7 - 3/40*a^6 + 1/5*a^5 + 1/5*a^4 - 9/40*a^3 - 2/5*a^2 - 1/4*a - 1/8', '1/80*a^10 - 1/80*a^9 - 1/16*a^7 - 3/80*a^6 - 1/20*a^5 - 13/80*a^4 + 17/80*a^3 - 9/20*a^2 - 23/80*a + 7/16', '1/160*a^11 + 1/160*a^9 - 1/160*a^8 + 3/80*a^7 - 3/32*a^6 + 7/160*a^5 + 1/5*a^4 - 5/32*a^3 - 47/160*a^2 - 11/80*a - 13/32', '1/160*a^12 - 1/160*a^10 + 1/160*a^9 - 1/80*a^8 - 1/32*a^7 - 3/160*a^6 + 3/20*a^5 + 17/160*a^4 + 3/32*a^3 + 21/80*a^2 + 29/160*a + 1/16', '1/160*a^13 - 1/160*a^10 + 1/160*a^9 - 1/80*a^8 - 7/160*a^7 - 17/160*a^6 - 1/4*a^5 - 3/32*a^4 + 3/32*a^3 - 11/80*a^2 - 5/16*a - 11/32']}
Number field data - 14.2.20325604337285010030592.1