-
nf_fields • Show schema
{'class_group': [14], 'class_number': 14, 'cm': False, 'coeffs': [-62041733, -9051406, -1559558, -97006, -7462, 0, 0, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 385348306064778857983, 'disc_rad': 3731, 'disc_sign': -1, 'frobs': [[2, [[3, 2], [1, 1]]], [3, [[6, 1], [1, 1]]], [5, [[6, 1], [1, 1]]], [7, [0]], [11, [[3, 2], [1, 1]]], [13, [0]], [17, [[6, 1], [1, 1]]], [19, [[6, 1], [1, 1]]], [23, [[3, 2], [1, 1]]], [29, [[7, 1]]], [31, [[6, 1], [1, 1]]], [37, [[3, 2], [1, 1]]], [41, [0]], [43, [[1, 7]]], [47, [[6, 1], [1, 1]]], [53, [[3, 2], [1, 1]]], [59, [[6, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [35, 36, 36], 'galois_label': '7T4', 'galt': 4, 'grd': 1100.1277440755782, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.1.385348306064778857983.1', 'local_algs': ['7.1.1.0a1.1', '7.1.6.5a1.1', '13.1.7.6a1.1', '41.1.7.6a1.1'], 'monogenic': 0, 'narrow_class_group': [14], 'narrow_class_number': 14, 'num_ram': 3, 'r2': 3, 'ramps': [7, 13, 41], 'rd': 872.6421931553961, 'regulator': {'__RealLiteral__': 0, 'data': '9464104.459419131', 'prec': 57}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( -\\frac{479651758254425106845819445881}{424098577} a^{6} - \\frac{11772751096412814940319586051170}{424098577} a^{5} - \\frac{288954778260043722524127366164965}{424098577} a^{4} - \\frac{3513052050401157566613207247989914}{424098577} a^{3} - \\frac{39696556369506506505701003461522099}{424098577} a^{2} - \\frac{226282292083615576135607816157898855}{424098577} a - \\frac{1212433831416014865481556930512555181}{424098577} \\)', '\\( -\\frac{66082313193897827285351586}{60585511} a^{6} + \\frac{549732704101538379865391929}{60585511} a^{5} + \\frac{25477919757633954545581664}{1236439} a^{4} + \\frac{411344689070789499474277270795}{60585511} a^{3} + \\frac{3159801572546022444808897018080}{60585511} a^{2} + \\frac{39859797252482190697162968467334}{60585511} a + \\frac{133681379755731148694451103131541}{60585511} \\)', '\\( \\frac{24103444009265841984149658624481768250472050309415977648410204572273775353}{8655073} a^{6} - \\frac{496356557633775937391922810088726893169855995036905812923455468952551286738}{60585511} a^{5} - \\frac{14310838596443990716115964425566276788878671128423801684447335552411125280441}{60585511} a^{4} - \\frac{1023557502796104569832148170503835448718385744817106763278557811629652066950602}{60585511} a^{3} - \\frac{13820347811603559794868195736793738092182929588078625813216406448642837136608383}{60585511} a^{2} - \\frac{122477752078415404219769310303146609253018016352659235093446168237708524369410171}{60585511} a - \\frac{806939585116751898868796351865465994894262613799332056544377472327608158837946253}{60585511} \\)'], 'used_grh': True, 'zk': ['1', 'a', '1/7*a^2 - 3/7*a - 3/7', '1/7*a^3 + 2/7*a - 2/7', '1/49*a^4 + 1/49*a^3 + 3/49*a^2 - 17/49*a - 5/49', '1/49*a^5 + 2/49*a^3 + 1/49*a^2 - 2/49*a - 9/49', '1/424098577*a^6 - 612880/424098577*a^5 + 381273/424098577*a^4 + 29677444/424098577*a^3 + 10484504/424098577*a^2 + 102061823/424098577*a - 61748966/424098577']}
Number field data - 7.1.385348306064778857983.1