Number field data - 5.1.16078125.1

Formats: - HTML - YAML - JSON - 2026-03-24T12:39:07.979661

• nf_fields •

  Column	Type
  class_group	jsonb
  class_number	numeric
  cm	boolean
  coeffs	numeric[]
  conductor	numeric
  degree	smallint
  disc_abs	numeric
  disc_rad	numeric
  disc_sign	smallint
  embeddings_gen_imag	double precision[]
  embeddings_gen_real	double precision[]
  gal_is_abelian	boolean
  gal_is_cyclic	boolean
  gal_is_solvable	boolean
  galois_disc_exponents	numeric[]
  galois_label	text
  galt	integer
  grd	double precision
  index	integer
  inessentialp	integer[]
  is_galois	boolean
  is_minimal_sibling	boolean
  iso_number	smallint
  label	text
  local_algs	text[]
  maximal_cm_subfield	numeric[]
  minimal_sibling	numeric[]
  monogenic	smallint
  narrow_class_group	bigint[]
  narrow_class_number	bigint
  num_ram	smallint
  r2	smallint
  ramps	numeric[]
  rd	double precision
  regulator	numeric
  relative_class_number	numeric
  subfield_mults	integer[]
  subfields	text[]
  torsion_order	smallint
  unit_signature_rank	smallint
  used_grh	boolean

  
  {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [6, 15, -25, 10, 0, 1], 'conductor': 0, 'degree': 5, 'disc_abs': 16078125, 'disc_rad': 105, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [60, 156, 100], 'galois_label': '5T5', 'galt': 5, 'grd': 71.034609880671, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '5.1.16078125.1', 'local_algs': ['3.1.1.0a1.1', '3.1.2.1a1.1', '3.2.1.0a1.1', '5.1.5.6a1.1', '7.1.2.1a1.1', '7.1.3.2a1.3'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 2, 'ramps': [3, 5, 7], 'rd': 27.6214885953, 'regulator': {'__RealLiteral__': 0, 'data': '184.634692508', 'prec': 44}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 1, 'used_grh': False}
• nf_fields_extra •

  Column	Type
  dirichlet_group	bigint[]
  frobs	jsonb
  label	text
  res	jsonb
  source	text
  subfield_inclusions	smallint[]
  torsion_gen	text
  torsion_gen_coeffs	numeric[]
  units	jsonb
  unitsGmodule	jsonb
  unitsType	text
  units_coeffs	numeric[]
  zk	jsonb

  
  {'dirichlet_group': [], 'frobs': [[2, [[4, 1], [1, 1]]], [3, [0]], [5, [0]], [7, [0]], [11, [[3, 1], [2, 1]]], [13, [[4, 1], [1, 1]]], [17, [[3, 1], [1, 2]]], [19, [[4, 1], [1, 1]]], [23, [[3, 1], [2, 1]]], [29, [[4, 1], [1, 1]]], [31, [[4, 1], [1, 1]]], [37, [[3, 1], [1, 2]]], [41, [[5, 1]]], [43, [[5, 1]]], [47, [[5, 1]]], [53, [[3, 1], [2, 1]]], [59, [[3, 1], [1, 2]]]], 'label': '5.1.16078125.1', 'res': {'sib': ['-104,-106,15,55,15,-1,1', '-405,1350,-4140,6600,-4800,5218,-230,970,740,100,-4,50,-30,-10,0,1', '-53235,136500,1006705,-1999585,-769475,5841122,-13030065,-9128910,29996425,6156230,-72263398,78156305,-17024955,-28865925,19715920,6521647,-12722865,4263265,1583995,-1509600,105888,306035,-149590,18050,8335,-3825,690,-115,40,-10,1', '-9,60,185,70,-20,83,15,-10,5,-5,1', '13996800,-116640000,718632000,-2844922500,7285525425,-13018145580,17376702300,-18280451970,15826707930,-11701033995,7623377569,-4475217865,2385508565,-1146704430,490621650,-186173768,64606175,-22473905,8737705,-3726590,1521143,-529055,147415,-33235,7830,-2954,1310,-450,105,-15,1', '1440000,-10800000,13080000,21240000,35830000,30690000,79200000,59035500,64227475,-23601950,8444535,29507150,52055150,-53252350,13671005,10591820,6860110,-17357170,23401100,-11642750,449539,332920,2623040,-4179040,3302600,-1107152,95665,6490,108370,-158170,90908,-22970,-2655,6840,-2650,-276,600,-280,80,-10,1', '252,-2310,-14945,51170,163905,131803,2725,-52700,-53080,14910,30368,-7985,-7435,4425,-310,-827,625,-245,60,-10,1', '286335,864675,-240030,-968625,2769165,674415,-3222750,2137830,132565,-1615735,1762964,-1274700,710998,-354620,179664,-91294,43740,-17773,6945,-2744,931,-270,62,-10,1', '295,-250,60,-210,50,-87,30,-10,10,0,1', '51216390,-116539425,635016555,-906017685,1929368185,-1890593703,621615645,-472273245,-690730895,623113475,554851991,-363761675,-188493155,107401265,53834155,-34568929,-4423845,5714075,-140025,-569815,33373,66505,-17865,-475,1495,-453,-15,25,5,-5,1', '729,-3645,5265,8235,-42210,35019,105300,-308310,392300,-263225,84572,-18355,16880,-10950,3105,-792,325,-70,10,-5,1', '8960,-67200,240800,-525700,757505,-737660,481500,-209305,68245,-22440,11139,-1125,-3610,3885,-1585,116,305,-185,60,-10,1', '960,-3168,1888,1200,-1880,410,441,-306,20,45,-15,-1,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{37}{17} a^{4} - \\frac{61}{17} a^{3} + \\frac{154}{17} a^{2} - \\frac{1937}{17} a - \\frac{661}{17} \\)', '\\( \\frac{771}{17} a^{4} + \\frac{2258}{17} a^{3} + \\frac{11715}{17} a^{2} + \\frac{8910}{17} a + \\frac{1585}{17} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/17*a^4 + 8/17*a^3 + 6/17*a^2 + 6/17*a - 5/17']}