Formats: - HTML - YAML - JSON - 2026-08-13T19:15:07.652205
  • nf_fields • Show schema
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [14, 30, 4, -12, -1, 1], 'conductor': 0, 'degree': 5, 'disc_abs': 13579520, 'disc_rad': 1030, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [260, 60, 60], 'galois_label': '5T5', 'galt': 5, 'grd': 101.89087030315206, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.5.13579520.1', 'local_algs': ['2.1.1.0a1.1', '2.1.4.8a1.1', '5.1.2.1a1.1', '5.3.1.0a1.1', '103.1.1.0a1.1', '103.1.2.1a1.2', '103.1.2.1a1.1'], 'maxp': 103, 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 0, 'ramps': [2, 5, 103], 'rd': 26.7040347087, 'regulator': {'__RealLiteral__': 0, 'data': '303.0791893', 'prec': 34}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 5, 'used_grh': False}
  • nf_fields_extra • Show schema
    {'dirichlet_group': [], 'frobs': [[2, [0]], [3, [[3, 1], [2, 1]]], [5, [0]], [7, [[4, 1], [1, 1]]], [11, [[3, 1], [1, 2]]], [13, [[3, 1], [2, 1]]], [17, [[4, 1], [1, 1]]], [19, [[5, 1]]], [23, [[3, 1], [2, 1]]], [29, [[5, 1]]], [31, [[3, 1], [1, 2]]], [37, [[4, 1], [1, 1]]], [41, [[5, 1]]], [43, [[4, 1], [1, 1]]], [47, [[3, 1], [2, 1]]], [53, [[2, 1], [1, 3]]], [59, [[5, 1]]]], 'label': '5.5.13579520.1', 'res': {'sib': ['-34,-40,32,28,-14,-2,1', '16,0,-512,0,992,0,-664,0,192,0,-24,0,1', '2,24,74,-16,-175,-10,101,12,-19,-2,1', '20,600,5396,19672,22258,-33928,-86922,-964,101057,31228,-57969,-23720,19008,8012,-3799,-1392,468,120,-33,-4,1', '3810648,-9866704,-3716480,25811840,-8750844,-23883616,15742000,9301584,-9849690,-889832,2968344,-405740,-437660,127272,26248,-13496,38,568,-48,-8,1', '4,832,22616,69416,-37504,-343048,-220208,474156,598445,-98148,-428954,-125056,88719,41840,-8784,-5352,597,328,-34,-8,1', '55,615,619,-918,-1141,133,321,6,-31,-1,1', '8,48,-80,-868,-1384,328,2208,884,-1104,-724,216,204,-14,-24,0,1', '11492100,0,-330144800,0,3857039616,0,-24426239888,0,95009445472,0,-243772273632,0,431480476572,0,-542391897880,0,493433401812,0,-328758718440,0,161557837428,0,-58770478888,0,15840588241,0,-3157370268,0,462678650,0,-49261880,0,3731503,0,-193960,0,6494,0,-124,0,1', '30684449,365712124,1660194578,3326356244,1667132907,-4086288936,-5771974634,67894072,3784919688,1202871364,-1102751446,-544515676,171254595,113622588,-15553430,-13560944,931236,988992,-46230,-44000,2147,1104,-70,-12,1', '668000,12768000,20196000,-214552000,-104764160,1158463520,-79365936,-2849760128,1141231040,3572201568,-2277512816,-2387587392,2104922880,837681184,-1099254224,-112492832,352734472,-22610720,-72070552,12706848,9378184,-2536232,-741908,282576,30090,-18448,-98,660,-38,-10,1', '8,-656,13816,-64912,-183084,1596112,-541494,-11929240,16498528,30604172,-72279132,-6928232,102653000,-33817564,-73546798,39800848,30885498,-21585476,-7987921,6882732,1240328,-1374704,-95815,172604,-762,-13032,765,524,-52,-8,1', '9536,-355520,2502848,-5391296,-5779328,39494912,-34040828,-74168864,141454624,19775024,-199226568,76417592,142377944,-101959384,-56320712,63315008,11146056,-23745144,-23944,5797760,-561960,-941160,147688,100372,-19620,-6708,1482,252,-60,-4,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{2}{3} a^{4} - a^{3} - 8 a^{2} + \\frac{23}{3} a + \\frac{53}{3} \\)', '\\( \\frac{1}{3} a^{4} - a^{3} - 2 a^{2} + \\frac{22}{3} a - \\frac{11}{3} \\)', '\\( \\frac{2}{3} a^{4} - 2 a^{3} - 6 a^{2} + \\frac{44}{3} a + \\frac{29}{3} \\)', '\\( \\frac{1}{3} a^{4} + a^{3} - 3 a^{2} - \\frac{35}{3} a - \\frac{23}{3} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4 + 1/3*a + 1/3']}