-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 2, -19, -15, 81, 37, -126, -32, 79, 8, -17, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2196839556078125, 'disc_rad': 1015, 'disc_sign': 1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [0]], [7, [0]], [11, [[6, 1], [3, 2]]], [13, [[2, 6]]], [17, [[12, 1]]], [19, [[6, 1], [3, 2]]], [23, [[6, 2]]], [29, [0]], [31, [[6, 1], [3, 2]]], [37, [[12, 1]]], [41, [[2, 3], [1, 6]]], [43, [[4, 3]]], [47, [[12, 1]]], [53, [[6, 2]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12, 16, 12], 'galois_label': '12T14', 'galt': 14, 'grd': 44.06387579995631, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.12.2196839556078125.1', 'local_algs': ['5.12.6.1', '7.6.4.3', '7.6.4.3', '29.2.1.2', '29.2.1.2', '29.2.0.1', '29.2.0.1', '29.2.0.1', '29.2.1.2'], 'monogenic': 0, 'num_ram': 3, 'r2': 0, 'ramps': [5, 7, 29], 'rd': 18.9881736599, 'regulator': {'__RealLiteral__': 0, 'data': '3668.73449811', 'prec': 44}, 'res': {'gal': ['169,2860,12521,-11639,-133103,-9659,537022,34676,-1092490,92820,1221211,-270957,-781464,258142,288660,-122740,-59220,31789,5808,-4452,-94,308,-22,-8,1'], 'sib': ['-7,91,-126,-510,444,624,-466,-250,179,33,-25,-1,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '1.-2.-1.1', '1.1.-3.-1.1', '-1.-2.7.2.-7.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{22}{13} a^{11} - \\frac{33}{13} a^{10} - \\frac{353}{13} a^{9} + \\frac{344}{13} a^{8} + 115 a^{7} - \\frac{1353}{13} a^{6} - 138 a^{5} + \\frac{1330}{13} a^{4} + \\frac{769}{13} a^{3} - \\frac{367}{13} a^{2} - \\frac{83}{13} a + \\frac{11}{13} \\)', '\\( \\frac{315}{533} a^{11} - \\frac{288}{533} a^{10} - \\frac{5170}{533} a^{9} + \\frac{1784}{533} a^{8} + \\frac{21738}{533} a^{7} - \\frac{5451}{533} a^{6} - \\frac{27022}{533} a^{5} - \\frac{582}{533} a^{4} + \\frac{12686}{533} a^{3} + \\frac{2954}{533} a^{2} - \\frac{58}{13} a - \\frac{272}{533} \\)', '\\( \\frac{272}{533} a^{11} + \\frac{43}{533} a^{10} - \\frac{4912}{533} a^{9} - \\frac{2994}{533} a^{8} + \\frac{23272}{533} a^{7} + \\frac{13034}{533} a^{6} - \\frac{39723}{533} a^{5} - \\frac{16958}{533} a^{4} + \\frac{1650}{41} a^{3} + \\frac{662}{41} a^{2} - \\frac{54}{13} a - \\frac{1834}{533} \\)', '\\( \\frac{424}{533} a^{11} - \\frac{1046}{533} a^{10} - \\frac{6152}{533} a^{9} + \\frac{13110}{533} a^{8} + \\frac{21980}{533} a^{7} - \\frac{52766}{533} a^{6} - \\frac{8919}{533} a^{5} + \\frac{54362}{533} a^{4} - \\frac{474}{41} a^{3} - \\frac{1334}{41} a^{2} + \\frac{42}{13} a + \\frac{684}{533} \\)', '\\( \\frac{315}{533} a^{11} - \\frac{288}{533} a^{10} - \\frac{5170}{533} a^{9} + \\frac{1784}{533} a^{8} + \\frac{21738}{533} a^{7} - \\frac{5451}{533} a^{6} - \\frac{27022}{533} a^{5} - \\frac{582}{533} a^{4} + \\frac{12686}{533} a^{3} + \\frac{2954}{533} a^{2} - \\frac{58}{13} a + \\frac{261}{533} \\)', '\\( \\frac{171}{533} a^{11} + \\frac{10}{533} a^{10} - \\frac{2625}{533} a^{9} - \\frac{2096}{533} a^{8} + \\frac{571}{41} a^{7} + \\frac{10927}{533} a^{6} + \\frac{242}{41} a^{5} - \\frac{23987}{533} a^{4} - \\frac{13495}{533} a^{3} + \\frac{14945}{533} a^{2} + \\frac{115}{13} a - \\frac{2651}{533} \\)', '\\( \\frac{294}{533} a^{11} - \\frac{564}{533} a^{10} - \\frac{4552}{533} a^{9} + \\frac{6678}{533} a^{8} + \\frac{18411}{533} a^{7} - \\frac{28064}{533} a^{6} - \\frac{18953}{533} a^{5} + \\frac{33372}{533} a^{4} + \\frac{7415}{533} a^{3} - \\frac{12689}{533} a^{2} - \\frac{32}{13} a + \\frac{61}{41} \\)', '\\( \\frac{628}{533} a^{11} - \\frac{1188}{533} a^{10} - \\frac{9344}{533} a^{9} + \\frac{13140}{533} a^{8} + \\frac{33325}{533} a^{7} - \\frac{48669}{533} a^{6} - \\frac{15741}{533} a^{5} + \\frac{33177}{533} a^{4} - \\frac{6536}{533} a^{3} - \\frac{986}{533} a^{2} + 5 a - \\frac{1163}{533} \\)', '\\( \\frac{1205}{533} a^{11} - \\frac{87}{41} a^{10} - \\frac{20145}{533} a^{9} + \\frac{8048}{533} a^{8} + \\frac{88793}{533} a^{7} - \\frac{2368}{41} a^{6} - \\frac{123031}{533} a^{5} + \\frac{2133}{41} a^{4} + \\frac{55430}{533} a^{3} - \\frac{4872}{533} a^{2} - \\frac{59}{13} a - \\frac{214}{533} \\)', '\\( \\frac{99}{533} a^{11} + \\frac{241}{533} a^{10} - \\frac{2070}{533} a^{9} - \\frac{4856}{533} a^{8} + \\frac{11151}{533} a^{7} + \\frac{21945}{533} a^{6} - \\frac{24779}{533} a^{5} - \\frac{31282}{533} a^{4} + \\frac{1410}{41} a^{3} + \\frac{1256}{41} a^{2} - \\frac{88}{13} a - \\frac{2631}{533} \\)', '\\( \\frac{389}{533} a^{11} - \\frac{440}{533} a^{10} - \\frac{476}{41} a^{9} + \\frac{3500}{533} a^{8} + \\frac{24430}{533} a^{7} - \\frac{12281}{533} a^{6} - \\frac{24075}{533} a^{5} + \\frac{5951}{533} a^{4} + \\frac{6373}{533} a^{3} - \\frac{596}{533} a^{2} + \\frac{3}{13} a + \\frac{327}{533} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/13*a^10 + 1/13*a^9 + 3/13*a^8 + 6/13*a^7 + 2/13*a^6 + 2/13*a^5 + 5/13*a^4 + 5/13*a^3 - 1/13*a^2 - 5/13*a + 5/13', '1/533*a^11 + 19/533*a^10 - 252/533*a^9 + 216/533*a^8 - 111/533*a^7 - 79/533*a^6 + 262/533*a^5 - 217/533*a^4 + 128/533*a^3 + 3/533*a^2 + 3/13*a + 207/533']}
Number field data - 12.12.2196839556078125.1