Formats: - HTML - YAML - JSON - 2026-09-22T11:57:40.813312
  • nf_fields • Show schema
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1308, -1635, -545, 0, 0, 1], 'conductor': 0, 'degree': 5, 'disc_abs': 1429226380125, 'disc_rad': 1635, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [140, 100, 96], 'galois_label': '5T5', 'galt': 5, 'grd': 587.5673647942456, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '5.1.1429226380125.2', 'local_algs': ['3.1.2.1a1.2', '3.1.3.3a1.1', '5.1.2.1a1.2', '5.1.3.2a1.1', '109.1.5.4a1.1'], 'maxp': 109, 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 2, 'ramps': [3, 5, 109], 'rd': 269.786494259, 'regulator': {'__RealLiteral__': 0, 'data': '55162.1290118', 'prec': 40}, 'subfield_mults': [], 'subfields': [], 'torsion_order': 2, 'unit_signature_rank': 1, 'used_grh': False}
  • nf_fields_extra • Show schema
    {'dirichlet_group': [], 'frobs': [[2, [[4, 1], [1, 1]]], [3, [0]], [5, [0]], [7, [[3, 1], [2, 1]]], [11, [[3, 1], [1, 2]]], [13, [[3, 1], [2, 1]]], [17, [[3, 1], [2, 1]]], [19, [[2, 2], [1, 1]]], [23, [[3, 1], [2, 1]]], [29, [[3, 1], [1, 2]]], [31, [[2, 2], [1, 1]]], [37, [[4, 1], [1, 1]]], [41, [[5, 1]]], [43, [[4, 1], [1, 1]]], [47, [[2, 1], [1, 3]]], [53, [[2, 1], [1, 3]]], [59, [[3, 1], [1, 2]]]], 'label': '5.1.1429226380125.2', 'res': {'sib': ['-130958903356118505,-40691722362535755,-84594035367507060,-8518413439049922,-6803692668805671,11042863175327040,2427634969090101,365788474029387,-300527235671310,-84105440304484,-19569877869474,693647358039,585459013938,179396845668,129672687513,8721675084,5985803157,-1916641491,-233311482,-73963344,6851532,2088869,-186942,48210,10589,5034,-249,-253,-12,0,1', '-23306,-2643,2310,105,-90,-3,1', '-32731248,-14190056,343032,83712,-71125,5232,2088,-436,-36,0,1', '-869,-2473,62,4887,-2605,190,-54,-14,11,-5,1', '106327569645,0,111550728042,0,16338728025,0,753007227,0,-6898118,0,-2104986,0,293178,0,43195,0,813,0,18,0,1', '241803929793,230370118752,-93870177065,-171507165615,-46582193130,25831943463,23687375439,7109709210,764067110,-213679785,-78913602,-14423534,534645,356430,118810,0,-654,-545,0,0,1', '34326920,-127670400,156625200,-56428425,-13158720,5128890,707877,-98556,-27984,12815,1416,492,-101,-24,0,1', '381989473752025,-5718811216715625,31867835722736550,-76489964173913515,54616573833458670,368568274385385,-13706892945101064,4386246582832515,-401687725496658,255268560822765,-154379212595604,27898779220875,1042936160090,-306730039395,-323108621250,38713639545,19337534412,-4549161135,647093934,-162214275,26633022,-6743425,2006040,-277155,62830,-16665,576,225,42,-15,1', '42576195600,0,-22967143020,0,3679008645,0,-285727535,0,29506099,0,-2761617,0,109970,0,-8455,0,525,0,-2,0,1', '5331481,0,2537616,0,312120,0,-41370,0,-960,0,-24,0,1', '55174594948321,-30251133598440,97749234702,15321315897700,-784217312031,-2477110027470,69171201590,491050142700,-8949703770,-19500161940,12521462007,-1543915680,589840274,137116050,-14597727,308430,2910840,-644580,173090,-18840,2829,-650,18,0,1', '6736506964121584319,-4732244872058165403,1612330504560320580,-178200272277410455,-283136426212731825,71032590475339419,11081154336950251,-6298126365789915,855551850122145,790391125632130,-52656087639669,-26583610670325,7431977176650,177859282860,-688146034875,-28199256475,16550470620,-3010942425,-602188485,116552610,2673225,-7841460,356430,178215,0,-1308,981,0,0,0,1', '79225826714442870532144,-23340566184969382660960,40245248189612701423832,-37619975068662734098742,28763084249559508179859,-13192861692067461936702,6655292405998200153071,-2324501839313391457406,1158509108143530588052,-540130322309943413338,290028811826318492183,-136168926045140827872,57814849778462510475,-21243942844019577282,7063563744945447177,-2039411566297086594,550378047450549543,-128246848629358404,28473215632286917,-5153536303129636,840880315745588,-90297384742934,8344258213957,-1515122538006,1278765452058,-624313723824,218204249037,-59733507246,14197822353,-3198704484,675123728,-128431256,21799036,-3228742,437528,-58836,9127,-1444,206,-20,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{1408007378960515526149219712376504}{25} a^{4} - \\frac{1227816921494914876092646177487568}{25} a^{3} + \\frac{330889648215010266029015981469266}{25} a^{2} - \\frac{765461259404590865525367599228854092}{25} a - \\frac{1639344812615372303179775209005591631}{25} \\)', '\\( \\frac{1354696870177344338030483389350239536271119203251168719414117626840766}{25} a^{4} - \\frac{4299334719141511906541787727797527692910610073427623720227527490699422}{25} a^{3} + \\frac{9554012523117783389198200158134958330519515000403566295774757454668074}{25} a^{2} - \\frac{756514457627468394825643328069036431282470408586573485209162895270294978}{25} a + \\frac{159698463539360361903005524607959811852515571331811708928539218403393841}{25} \\)'], 'zk': ['1', 'a', '1/5*a^2 - 1/5*a - 1/5', '1/5*a^3 - 2/5*a - 1/5', '1/25*a^4 - 2/25*a^3 - 1/25*a^2 + 2/25*a + 1/25']}