-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, 1, 1, 4, 3, -22, -31, -69, -42, 72, 160, 277, 152, 27, 37, -18, -35, 3, -13, 1, 2, -1, 1], 'conductor': 0, 'degree': 22, 'dirichlet_group': [], 'disc_abs': 1734677982017693835986328125, 'disc_rad': 29801931595, 'disc_sign': 1, 'frobs': [[2, [[22, 1]]], [3, [[6, 1], [4, 4]]], [5, [0]], [7, [[22, 1]]], [11, [[5, 2], [4, 2], [2, 2]]], [13, [[10, 1], [4, 2], [2, 2]]], [17, [[22, 1]]], [19, [[6, 2], [3, 2], [2, 2]]], [23, [[18, 1], [2, 2]]], [29, [[8, 2], [3, 2]]], [31, [[5, 2], [2, 4], [1, 4]]], [37, [[10, 2], [2, 1]]], [41, [[7, 2], [2, 2], [1, 4]]], [43, [[10, 1], [4, 2], [2, 2]]], [47, [[8, 2], [6, 1]]], [53, [[6, 1], [4, 2], [2, 4]]], [59, [[11, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [39916800, 39916800, 39916800], 'galois_label': '22T47', 'galt': 47, 'grd': 172632.35964036407, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '22.2.1734677982017693835986328125.1', 'local_algs': ['5.6.3.1', '5.6.3.1', '5.10.5.1', 'm64661.1.1.0', 'm64661.1.1.0', 'm64661.2.1.1', 'm64661.2.1.1', 'm64661.1.3.0', 'm64661.1.3.0', 'm64661.1.5.0', 'm64661.1.5.0', 'm92179.1.2.0', 'm92179.1.2.0', 'm92179.2.1.1', 'm92179.2.1.1', 'm92179.1.3.0', 'm92179.1.3.0', 'm92179.1.4.0', 'm92179.1.4.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 10, 'ramps': [5, 64661, 92179], 'rd': 17.3039922569, 'regulator': {'__RealLiteral__': 0, 'data': '38336.3977164', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '1.1.0.1.0.-2.1.-2.0.1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1319022478040683642982}{2124470127291230454011} a^{21} - 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\\frac{57269428450016078602307}{2124470127291230454011} a^{6} - \\frac{29610828861680852745196}{2124470127291230454011} a^{5} - \\frac{47216961417063176314245}{2124470127291230454011} a^{4} - \\frac{5837116242752313623986}{2124470127291230454011} a^{3} + \\frac{3128805992904415407293}{2124470127291230454011} a^{2} + \\frac{1208064985250560700296}{2124470127291230454011} a + \\frac{4869117827277084875008}{2124470127291230454011} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', 'a^15', 'a^16', 'a^17', 'a^18', 'a^19', 'a^20', '1/2124470127291230454011*a^21 + 432162695892207561224/2124470127291230454011*a^20 - 653641761206245262533/2124470127291230454011*a^19 + 167982702717637181560/2124470127291230454011*a^18 + 532665987662589956145/2124470127291230454011*a^17 + 625983005593256221797/2124470127291230454011*a^16 - 463273244278987969270/2124470127291230454011*a^15 - 518926591257159751500/2124470127291230454011*a^14 + 508818139788462937089/2124470127291230454011*a^13 + 749396289026961292787/2124470127291230454011*a^12 + 856956959840666211577/2124470127291230454011*a^11 + 556372178049218564352/2124470127291230454011*a^10 + 828731590687777909608/2124470127291230454011*a^9 - 463905878846124332921/2124470127291230454011*a^8 + 215007940286959093640/2124470127291230454011*a^7 - 674937675082602811008/2124470127291230454011*a^6 - 243201499321128170322/2124470127291230454011*a^5 - 616326127851568785886/2124470127291230454011*a^4 - 832659424940701796791/2124470127291230454011*a^3 - 819262980435466447033/2124470127291230454011*a^2 + 1046535151217522863157/2124470127291230454011*a + 930991225635280714244/2124470127291230454011']}
Number field data - 22.2.1734677982017693835986328125.1