-
nf_fields • Show schema
{'class_group': [2, 2, 50], 'class_number': 200, 'cm': False, 'coeffs': [1048631, -129244, -35251, 3618, -1409, 16, 51, -2, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 106837547250625, 'disc_rad': 3215, 'disc_sign': 1, 'frobs': [[2, [[4, 2]]], [3, [[4, 2]]], [5, [0]], [7, [[6, 1], [2, 1]]], [11, [[4, 2]]], [13, [[4, 2]]], [17, [[4, 2]]], [19, [[4, 2]]], [23, [[6, 1], [2, 1]]], [29, [[3, 2], [1, 2]]], [31, [[3, 2], [1, 2]]], [37, [[2, 2], [1, 4]]], [41, [[4, 2]]], [43, [[2, 2], [1, 4]]], [47, [[2, 2], [1, 4]]], [53, [[6, 1], [2, 1]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 24], 'galois_label': '8T24', 'galt': 24, 'grd': 56.70097000933934, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 3, 'label': '8.0.106837547250625.3', 'local_algs': ['5.2.1.2', '5.2.1.2', '5.4.2.1', 'm643.2.1.1', 'm643.2.1.1', 'm643.2.2.2'], 'minimal_sibling': [-1, -1, 4, -22, -4, -1, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 4, 'ramps': [5, 643], 'rd': 56.7009700093, 'regulator': {'__RealLiteral__': 0, 'data': '26.1311328719', 'prec': 44}, 'res': {'sib': ['5489,-139,650,-38,44,-3,1', '-1,-1,4,-22,-4,-1,1', '-39595,8670,64529,-129848,134635,-111356,77560,-67849,62629,-32157,20376,-15376,9436,-7710,5972,-3605,1906,-871,432,-249,134,-72,33,-9,1', '-865,-3330,4691,-1684,340,-1018,368,-15,81,-25,0,-3,1', '1,0,3,20,8,5,-4,-5,8,-20,3,0,1', '1,2,-4,4,1,-8,-1,-1,1', '1102109,-597598,2985099,-6307666,7785470,-8022696,7491927,-5672092,3660611,-2073310,1146123,-574536,204996,406,-46204,22212,-116,-3732,782,588,-259,-44,50,-12,1', '1258849,381618,5507426,-84094,-343500,-7529184,326777,2094000,3440818,145084,-451090,-287146,69537,29058,-9030,-7764,1808,2240,-113,-366,-58,56,10,-8,1', '18769,0,11914,0,7479,0,943,0,131,0,14,0,1', '21696,10096,-15568,-10688,7782,-567,1587,-573,108,-68,18,0,1', '2253001,0,267830,0,-33909,0,-1477,0,299,0,-26,0,1', '300464,1962584,2636104,-2083176,204709,111310,-39271,70334,-351,5704,-451,-390,91,-74,16,-4,1', '65739664,0,41004036,0,-12459403,0,-2763456,0,2998138,0,-424302,0,4905,0,-33384,0,18589,0,-4266,0,538,0,-36,0,1', '9871,-3833,12478,-2869,3647,-859,508,-174,68,-16,7,0,1']}, 'subfield_mults': [1, 1], 'subfields': ['804.-1.1', '1.-2.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{28632970983}{3742958865918907} a^{7} + \\frac{219796661681}{7485917731837814} a^{6} + \\frac{1509909628296}{3742958865918907} a^{5} + \\frac{13001219680596}{3742958865918907} a^{4} - \\frac{14314743491684}{3742958865918907} a^{3} + \\frac{58878871171873}{3742958865918907} a^{2} - \\frac{628735156131437}{7485917731837814} a - \\frac{9514167683969859}{3742958865918907} \\)', '\\( \\frac{29213579093}{7485917731837814} a^{7} - \\frac{549119684}{3742958865918907} a^{6} + \\frac{964367601906}{3742958865918907} a^{5} + \\frac{6575264928325}{3742958865918907} a^{4} - \\frac{1334848960560}{3742958865918907} a^{3} + \\frac{538232325889891}{7485917731837814} a^{2} - \\frac{246295542369046}{3742958865918907} a - \\frac{3489543683096214}{3742958865918907} \\)', '\\( \\frac{1146812609619}{7485917731837814} a^{7} - \\frac{8027492574317}{7485917731837814} a^{6} + \\frac{96653625299013}{7485917731837814} a^{5} - \\frac{447948985837937}{7485917731837814} a^{4} + \\frac{411790185548225}{7485917731837814} a^{3} + \\frac{1787846118958584}{3742958865918907} a^{2} - \\frac{32806550577413515}{3742958865918907} a + \\frac{110279683959529222}{3742958865918907} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2', '1/2*a^5 - 1/2', '1/2*a^6 - 1/2*a', '1/7485917731837814*a^7 + 763294146835823/7485917731837814*a^6 + 1246548555042167/7485917731837814*a^5 - 129997295730519/7485917731837814*a^4 - 826343920726973/7485917731837814*a^3 + 565270584825377/3742958865918907*a^2 - 344777135831268/3742958865918907*a + 1721600965202492/3742958865918907']}
Number field data - 8.0.106837547250625.3