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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -7, 20, 110, -69, -475, 58, 1031, 42, -1396, -52, 1297, -123, -799, 251, 260, -160, -12, 33, -10, 1], 'conductor': 0, 'degree': 20, 'dirichlet_group': [], 'disc_abs': 22993730893173532944527721, 'disc_rad': 68834471133, 'disc_sign': 1, 'frobs': [[2, [[10, 2]]], [3, [0]], [5, [[10, 2]]], [7, [[6, 1], [4, 1], [3, 2], [2, 2]]], [11, [[12, 1], [2, 4]]], [13, [[8, 1], [4, 3]]], [17, [[20, 1]]], [19, [[4, 2], [3, 4]]], [23, [[10, 2]]], [29, [[16, 1], [2, 1], [1, 2]]], [31, [[4, 3], [2, 4]]], [37, [[12, 1], [4, 2]]], [41, [[10, 2]]], [43, [[4, 1], [3, 4], [2, 2]]], [47, [[4, 4], [2, 2]]], [53, [[6, 1], [3, 2], [2, 2], [1, 4]]], [59, [[8, 2], [4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [1966080, 1966080, 1966080, 1966080], 'galois_label': '20T1015', 'galt': 1015, 'grd': 262363.2427246622, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '20.8.22993730893173532944527721.1', 'local_algs': ['3.4.0.1', '3.4.0.1', '3.12.6.2', '61.1.0.1', '61.1.0.1', '61.2.1.2', '61.2.0.1', '61.2.0.1', '61.4.0.1', '61.8.0.1', 'm11119.2.1.1', 'm11119.2.1.1', 'm11119.2.2.2', 'm11119.1.6.0', 'm11119.1.6.0', 'm33829.1.2.0', 'm33829.2.1.1', 'm33829.1.4.0', 'm33829.1.4.0', 'm33829.1.8.0'], 'monogenic': 0, 'num_ram': 4, 'r2': 6, 'ramps': [3, 61, 11119, 33829], 'rd': 18.5387510375, 'regulator': {'__RealLiteral__': 0, 'data': '99704.5727669', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['1.-3.1.1.-2.1', '1.3.-1.-2.0.-3.1.5.-2.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{11} a^{18} - \\frac{9}{11} a^{17} + \\frac{30}{11} a^{16} - \\frac{36}{11} a^{15} - \\frac{38}{11} a^{14} + \\frac{182}{11} a^{13} - \\frac{191}{11} a^{12} - \\frac{206}{11} a^{11} + \\frac{648}{11} a^{10} - \\frac{17}{11} a^{9} - \\frac{1065}{11} a^{8} + 18 a^{7} + \\frac{1154}{11} a^{6} - \\frac{59}{11} a^{5} - \\frac{799}{11} a^{4} - 11 a^{3} + \\frac{263}{11} a^{2} + \\frac{65}{11} a - \\frac{20}{11} \\)', '\\( a^{2} - a - 1 \\)', '\\( \\frac{3}{11} a^{18} - \\frac{27}{11} a^{17} + \\frac{68}{11} a^{16} + \\frac{68}{11} a^{15} - \\frac{521}{11} a^{14} + \\frac{315}{11} a^{13} + \\frac{1418}{11} a^{12} - \\frac{1553}{11} a^{11} - \\frac{2214}{11} a^{10} + \\frac{2831}{11} a^{9} + \\frac{2569}{11} a^{8} - 259 a^{7} - \\frac{2302}{11} a^{6} + \\frac{1605}{11} a^{5} + \\frac{1332}{11} a^{4} - 40 a^{3} - \\frac{366}{11} a^{2} + \\frac{63}{11} a + \\frac{28}{11} \\)', '\\( \\frac{8}{11} a^{18} - \\frac{72}{11} a^{17} + \\frac{196}{11} a^{16} + \\frac{64}{11} a^{15} - \\frac{1118}{11} a^{14} + \\frac{994}{11} a^{13} + \\frac{2443}{11} a^{12} - \\frac{3452}{11} a^{11} - \\frac{3209}{11} a^{10} + \\frac{5408}{11} a^{9} + \\frac{3437}{11} a^{8} - 452 a^{7} - \\frac{3088}{11} a^{6} + \\frac{2663}{11} a^{5} + \\frac{1792}{11} a^{4} - 61 a^{3} - \\frac{481}{11} a^{2} + \\frac{58}{11} a + \\frac{27}{11} \\)', '\\( a^{18} - 9 a^{17} + 25 a^{16} + 4 a^{15} - 130 a^{14} + 126 a^{13} + 266 a^{12} - 400 a^{11} - 342 a^{10} + 610 a^{9} + 367 a^{8} - 558 a^{7} - 327 a^{6} + 295 a^{5} + 190 a^{4} - 72 a^{3} - 50 a^{2} + 4 a + 2 \\)', '\\( \\frac{6}{11} a^{18} - \\frac{54}{11} a^{17} + \\frac{147}{11} a^{16} + \\frac{48}{11} a^{15} - \\frac{833}{11} a^{14} + \\frac{707}{11} a^{13} + \\frac{1901}{11} a^{12} - \\frac{2501}{11} a^{11} - \\frac{2756}{11} a^{10} + \\frac{4078}{11} a^{9} + \\frac{3213}{11} a^{8} - 351 a^{7} - \\frac{3009}{11} a^{6} + \\frac{2011}{11} a^{5} + \\frac{1850}{11} a^{4} - 38 a^{3} - \\frac{523}{11} a^{2} - \\frac{6}{11} a + \\frac{23}{11} \\)', '\\( \\frac{14}{11} a^{19} - \\frac{126}{11} a^{18} + \\frac{343}{11} a^{17} + \\frac{112}{11} a^{16} - \\frac{1951}{11} a^{15} + \\frac{1701}{11} a^{14} + \\frac{4344}{11} a^{13} - \\frac{5953}{11} a^{12} - \\frac{5965}{11} a^{11} + \\frac{9486}{11} a^{10} + \\frac{6650}{11} a^{9} - 803 a^{8} - \\frac{6097}{11} a^{7} + \\frac{4674}{11} a^{6} + \\frac{3631}{11} a^{5} - 97 a^{4} - \\frac{982}{11} a^{3} + \\frac{19}{11} a^{2} + \\frac{39}{11} a \\)', '\\( \\frac{1}{11} a^{19} - \\frac{10}{11} a^{18} + \\frac{39}{11} a^{17} - 6 a^{16} - \\frac{2}{11} a^{15} + 20 a^{14} - \\frac{384}{11} a^{13} + \\frac{62}{11} a^{12} + \\frac{700}{11} a^{11} - \\frac{742}{11} a^{10} - \\frac{498}{11} a^{9} + \\frac{1054}{11} a^{8} + \\frac{186}{11} a^{7} - \\frac{872}{11} a^{6} + \\frac{19}{11} a^{5} + \\frac{480}{11} a^{4} - \\frac{100}{11} a^{3} - 15 a^{2} + \\frac{36}{11} a + \\frac{20}{11} \\)', '\\( \\frac{4}{11} a^{19} - \\frac{35}{11} a^{18} + \\frac{89}{11} a^{17} + \\frac{62}{11} a^{16} - \\frac{584}{11} a^{15} + \\frac{382}{11} a^{14} + \\frac{1541}{11} a^{13} - \\frac{1741}{11} a^{12} - \\frac{2498}{11} a^{11} + \\frac{3341}{11} a^{10} + \\frac{3027}{11} a^{9} - \\frac{3705}{11} a^{8} - \\frac{2908}{11} a^{7} + \\frac{2425}{11} a^{6} + \\frac{1981}{11} a^{5} - \\frac{843}{11} a^{4} - \\frac{730}{11} a^{3} + \\frac{116}{11} a^{2} + \\frac{95}{11} a - \\frac{9}{11} \\)', '\\( \\frac{2}{11} a^{19} - a^{18} - \\frac{14}{11} a^{17} + \\frac{193}{11} a^{16} - \\frac{273}{11} a^{15} - \\frac{584}{11} a^{14} + \\frac{1431}{11} a^{13} + 68 a^{12} - \\frac{3105}{11} a^{11} - \\frac{811}{11} a^{10} + \\frac{4076}{11} a^{9} + \\frac{1268}{11} a^{8} - \\frac{3379}{11} a^{7} - \\frac{1588}{11} a^{6} + \\frac{1443}{11} a^{5} + \\frac{1062}{11} a^{4} - \\frac{123}{11} a^{3} - \\frac{251}{11} a^{2} - \\frac{58}{11} a + \\frac{3}{11} \\)', '\\( \\frac{4}{11} a^{19} - \\frac{30}{11} a^{18} + 4 a^{17} + \\frac{190}{11} a^{16} - \\frac{599}{11} a^{15} - \\frac{138}{11} a^{14} + \\frac{2077}{11} a^{13} - \\frac{870}{11} a^{12} - \\frac{3682}{11} a^{11} + \\frac{2148}{11} a^{10} + \\frac{4383}{11} a^{9} - \\frac{2177}{11} a^{8} - \\frac{3832}{11} a^{7} + 95 a^{6} + \\frac{2192}{11} a^{5} - \\frac{42}{11} a^{4} - \\frac{631}{11} a^{3} - \\frac{131}{11} a^{2} + \\frac{13}{11} a + \\frac{12}{11} \\)', '\\( \\frac{4}{11} a^{19} - \\frac{46}{11} a^{18} + \\frac{188}{11} a^{17} - \\frac{213}{11} a^{16} - \\frac{639}{11} a^{15} + \\frac{1900}{11} a^{14} - \\frac{54}{11} a^{13} - \\frac{4744}{11} a^{12} + \\frac{2837}{11} a^{11} + \\frac{6487}{11} a^{10} - \\frac{5289}{11} a^{9} - \\frac{6257}{11} a^{8} + \\frac{5045}{11} a^{7} + \\frac{4537}{11} a^{6} - \\frac{2870}{11} a^{5} - \\frac{2152}{11} a^{4} + \\frac{920}{11} a^{3} + \\frac{501}{11} a^{2} - \\frac{147}{11} a - \\frac{20}{11} \\)', '\\( \\frac{8}{11} a^{19} - \\frac{76}{11} a^{18} + \\frac{232}{11} a^{17} - \\frac{34}{11} a^{16} - \\frac{1150}{11} a^{15} + \\frac{1553}{11} a^{14} + \\frac{1946}{11} a^{13} - \\frac{4679}{11} a^{12} - \\frac{1461}{11} a^{11} + 639 a^{10} + \\frac{579}{11} a^{9} - \\frac{6630}{11} a^{8} - \\frac{250}{11} a^{7} + \\frac{4020}{11} a^{6} + \\frac{48}{11} a^{5} - \\frac{1457}{11} a^{4} + \\frac{168}{11} a^{3} + \\frac{304}{11} a^{2} - \\frac{90}{11} a - \\frac{19}{11} \\)'], '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', '1/11*a^18 + 2/11*a^17 - 3/11*a^16 - 3/11*a^15 - 5/11*a^14 - 5/11*a^13 - 4/11*a^12 + 3/11*a^11 - 1/11*a^10 + 5/11*a^9 + 2/11*a^8 - 1/11*a^6 - 4/11*a^5 + 4/11*a^4 - 1/11*a^2 - 1/11*a + 2/11', '1/11*a^19 + 4/11*a^17 + 3/11*a^16 + 1/11*a^15 + 5/11*a^14 - 5/11*a^13 + 4/11*a^11 - 4/11*a^10 + 3/11*a^9 - 4/11*a^8 - 1/11*a^7 - 2/11*a^6 + 1/11*a^5 + 3/11*a^4 - 1/11*a^3 + 1/11*a^2 + 4/11*a - 4/11']}
Number field data - 20.8.22993730893173532944527721.1