-
nf_fields • Show schema
{'class_group': [5], 'class_number': 5, 'cm': False, 'coeffs': [161051, 0, 0, 0, 0, -2904, 0, 0, 0, 0, 781, 0, 0, 0, 0, -54, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 20, 'disc_abs': 23383113568432629108428955078125, 'disc_rad': 55, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [135, 80], 'galois_label': '20T26', 'galt': 26, 'grd': 59.80309407631675, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '20.0.23383113568432629108428955078125.2', 'local_algs': ['5.1.20.27a1.1', '11.1.1.0a1.1', '11.1.1.0a1.1', '11.1.1.0a1.1', '11.1.1.0a1.1', '11.1.1.0a1.1', '11.1.5.4a1.5', '11.1.5.4a1.5', '11.1.5.4a1.5'], 'maximal_cm_subfield': [1, -1, 1, -1, 1], 'maxp': 11, 'monogenic': -1, 'narrow_class_group': [5], 'narrow_class_number': 5, 'num_ram': 2, 'r2': 10, 'ramps': [5, 11], 'rd': 37.020741826, 'regulator': {'__RealLiteral__': 0, 'data': '69020367.6146', 'prec': 44}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '1.-1.1.-1.1'], 'torsion_order': 10, 'unit_signature_rank': 0, 'used_grh': True} -
nf_fields_extra • Show schema
{'dirichlet_group': [], 'frobs': [[2, [[4, 5]]], [3, [[4, 5]]], [5, [0]], [7, [[4, 5]]], [11, [0]], [13, [[4, 5]]], [17, [[4, 5]]], [19, [[10, 2]]], [23, [[4, 5]]], [29, [[10, 2]]], [31, [[5, 3], [1, 5]]], [37, [[4, 5]]], [41, [[5, 3], [1, 5]]], [43, [[4, 5]]], [47, [[4, 5]]], [53, [[4, 5]]], [59, [[10, 2]]]], 'label': '20.0.23383113568432629108428955078125.2', 'res': {}, 'torsion_gen': '\\( \\frac{53}{732050} a^{15} - \\frac{629}{732050} a^{10} - \\frac{3041}{66550} a^{5} + \\frac{11}{25} \\)', 'units': ['\\( \\frac{6}{73205} a^{15} - \\frac{247}{73205} a^{10} - \\frac{84}{6655} a^{5} \\)', '\\( \\frac{3}{73205} a^{19} - \\frac{2}{366025} a^{18} - \\frac{9}{146410} a^{17} + \\frac{59}{366025} a^{16} - \\frac{1}{29282} a^{15} - \\frac{876}{366025} a^{14} + \\frac{81}{73205} a^{13} + \\frac{1913}{732050} a^{12} - \\frac{3538}{366025} a^{11} + \\frac{3913}{732050} a^{10} + \\frac{1312}{33275} a^{9} - \\frac{1919}{33275} a^{8} - \\frac{151}{66550} a^{7} + \\frac{4619}{33275} a^{6} - \\frac{19131}{66550} a^{5} - \\frac{276}{3025} a^{4} + \\frac{201}{275} a^{3} - \\frac{361}{275} a^{2} - \\frac{1}{5} a + \\frac{79}{25} \\)', '\\( \\frac{4}{366025} a^{19} + \\frac{1}{33275} a^{18} + \\frac{7}{146410} a^{17} + \\frac{61}{732050} a^{16} + \\frac{14}{366025} a^{15} - \\frac{29}{366025} a^{14} - \\frac{3}{2662} a^{13} - \\frac{307}{366025} a^{12} - \\frac{701}{366025} a^{11} + \\frac{311}{366025} a^{10} - \\frac{194}{33275} a^{9} + \\frac{79}{6050} a^{8} - \\frac{36}{33275} a^{7} + \\frac{178}{33275} a^{6} - \\frac{559}{33275} a^{5} + \\frac{29}{3025} a^{4} - \\frac{101}{550} a^{3} - \\frac{59}{550} a^{2} - \\frac{1}{2} a - \\frac{11}{25} \\)', '\\( \\frac{1}{146410} a^{19} - \\frac{2}{366025} a^{18} - \\frac{1}{73205} a^{17} + \\frac{61}{732050} a^{16} - \\frac{38}{366025} a^{15} - \\frac{102}{366025} a^{14} + \\frac{284}{366025} a^{13} - \\frac{137}{366025} a^{12} - \\frac{701}{366025} a^{11} + \\frac{677}{366025} a^{10} + \\frac{54}{33275} a^{9} - \\frac{357}{33275} a^{8} + \\frac{59}{33275} a^{7} + \\frac{178}{33275} a^{6} + \\frac{179}{6655} a^{5} - \\frac{809}{6050} a^{4} - \\frac{1}{55} a^{3} + \\frac{3}{275} a^{2} - \\frac{1}{2} a + \\frac{1}{25} \\)', '\\( \\frac{1}{366025} a^{19} - \\frac{3}{732050} a^{18} - \\frac{7}{146410} a^{17} - \\frac{1}{366025} a^{16} + \\frac{38}{366025} a^{15} + \\frac{123}{732050} a^{14} + \\frac{63}{732050} a^{13} + \\frac{307}{366025} a^{12} - \\frac{161}{146410} a^{11} - \\frac{677}{366025} a^{10} - \\frac{57}{66550} a^{9} + \\frac{823}{66550} a^{8} + \\frac{36}{33275} a^{7} + \\frac{391}{66550} a^{6} - \\frac{179}{6655} a^{5} - \\frac{463}{6050} a^{4} - \\frac{24}{275} a^{3} + \\frac{59}{550} a^{2} - \\frac{9}{50} a - \\frac{1}{25} \\)', '\\( \\frac{7}{366025} a^{19} - \\frac{1}{33275} a^{18} + \\frac{1}{73205} a^{17} - \\frac{1}{366025} a^{16} - \\frac{47}{366025} a^{15} - \\frac{503}{732050} a^{14} + \\frac{3}{2662} a^{13} + \\frac{137}{366025} a^{12} - \\frac{161}{146410} a^{11} + \\frac{1713}{366025} a^{10} + \\frac{269}{66550} a^{9} - \\frac{79}{6050} a^{8} - \\frac{59}{33275} a^{7} + \\frac{391}{66550} a^{6} - \\frac{183}{6655} a^{5} - \\frac{59}{1210} a^{4} + \\frac{101}{550} a^{3} - \\frac{3}{275} a^{2} - \\frac{9}{50} a + \\frac{14}{25} \\)', '\\( \\frac{4}{73205} a^{19} - \\frac{3}{73205} a^{18} - \\frac{13}{146410} a^{17} + \\frac{151}{732050} a^{16} - \\frac{13}{73205} a^{15} - \\frac{1146}{366025} a^{14} + \\frac{2203}{732050} a^{13} + \\frac{2333}{732050} a^{12} - \\frac{182}{14641} a^{11} + \\frac{11563}{732050} a^{10} + \\frac{1667}{33275} a^{9} - \\frac{5421}{66550} a^{8} + \\frac{899}{66550} a^{7} + \\frac{5356}{33275} a^{6} - \\frac{27341}{66550} a^{5} + \\frac{19}{275} a^{4} + \\frac{493}{550} a^{3} - \\frac{411}{275} a^{2} + \\frac{37}{50} a + \\frac{123}{50} \\)', '\\( \\frac{3}{73205} a^{19} - \\frac{16}{366025} a^{18} - \\frac{89}{732050} a^{17} + \\frac{37}{366025} a^{16} + \\frac{271}{732050} a^{15} - \\frac{876}{366025} a^{14} + \\frac{457}{366025} a^{13} + \\frac{1003}{146410} a^{12} - \\frac{2159}{732050} a^{11} - \\frac{1404}{73205} a^{10} + \\frac{1312}{33275} a^{9} + \\frac{609}{33275} a^{8} - \\frac{7323}{66550} a^{7} - \\frac{1399}{66550} a^{6} + \\frac{11171}{33275} a^{5} - \\frac{276}{3025} a^{4} - \\frac{43}{55} a^{3} + \\frac{96}{275} a^{2} + \\frac{89}{50} a - \\frac{123}{50} \\)', '\\( \\frac{23}{732050} a^{19} + \\frac{16}{366025} a^{18} - \\frac{9}{146410} a^{17} - \\frac{59}{366025} a^{16} - \\frac{119}{732050} a^{15} - \\frac{1407}{732050} a^{14} - \\frac{457}{366025} a^{13} + \\frac{1501}{366025} a^{12} + \\frac{3538}{366025} a^{11} + \\frac{7339}{732050} a^{10} + \\frac{317}{13310} a^{9} - \\frac{609}{33275} a^{8} - \\frac{3777}{33275} a^{7} - \\frac{4619}{33275} a^{6} - \\frac{7651}{66550} a^{5} + \\frac{797}{3025} a^{4} + \\frac{43}{55} a^{3} + \\frac{527}{550} a^{2} + \\frac{1}{5} a - \\frac{87}{25} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/5*a^7 - 2/5*a^6 + 1/5*a^5 - 1/5*a^2 + 2/5*a - 1/5', '1/5*a^8 + 2/5*a^6 + 2/5*a^5 - 1/5*a^3 - 2/5*a - 2/5', '1/5*a^9 + 1/5*a^6 - 2/5*a^5 - 1/5*a^4 - 1/5*a + 2/5', '1/110*a^10 + 23/110*a^5 + 1/10', '1/110*a^11 + 23/110*a^6 + 1/10*a', '1/1210*a^12 - 21/1210*a^7 - 1/5*a^6 - 2/5*a^5 - 5/22*a^2 + 1/5*a + 2/5', '1/1210*a^13 - 21/1210*a^8 + 1/5*a^6 + 1/5*a^5 - 5/22*a^3 - 1/5*a - 1/5', '1/66550*a^14 + 1/6050*a^13 + 1/6050*a^12 + 1/550*a^11 + 1/550*a^10 - 5587/66550*a^9 + 463/6050*a^8 + 463/6050*a^7 - 87/550*a^6 - 87/550*a^5 + 1801/6050*a^4 + 151/550*a^3 + 151/550*a^2 + 1/50*a + 1/50', '1/732050*a^15 - 263/732050*a^10 - 28207/66550*a^5 + 2/25', '1/732050*a^16 - 263/732050*a^11 - 28207/66550*a^6 + 2/25*a', '1/732050*a^17 - 263/732050*a^12 - 1587/66550*a^7 + 1/5*a^6 + 2/5*a^5 - 8/25*a^2 - 1/5*a - 2/5', '1/732050*a^18 - 263/732050*a^13 - 1587/66550*a^8 - 1/5*a^6 - 1/5*a^5 - 8/25*a^3 + 1/5*a + 1/5', '1/732050*a^19 + 1/732050*a^14 - 1/6050*a^13 - 1/6050*a^12 - 1/550*a^11 - 1/550*a^10 - 103/2662*a^9 - 463/6050*a^8 - 463/6050*a^7 - 243/550*a^6 + 197/550*a^5 - 531/3025*a^4 - 151/550*a^3 - 151/550*a^2 - 21/50*a - 11/50']}
Number field data - 20.0.23383113568432629108428955078125.2