-
nf_fields • Show schema
{'class_group': [3, 3, 3, 3, 6, 18], 'class_number': 8748, 'cm': False, 'coeffs': [40353607, 0, 0, -184875000, 0, 0, 313150767, 0, 0, 1705300, 0, 0, -28551, 0, 0, -60, 0, 0, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 8969580780515349163336915861800987000000000000, 'disc_rad': 570, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[3, 6]]], [11, [[6, 3]]], [13, [[3, 6]]], [17, [[2, 9]]], [19, [0]], [23, [[6, 3]]], [29, [[6, 3]]], [31, [[3, 3], [1, 9]]], [37, [[3, 6]]], [41, [[6, 3]]], [43, [[3, 3], [1, 9]]], [47, [[6, 3]]], [53, [[2, 9]]], [59, [[6, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 121, 36, 36], 'galois_label': '18T23', 'galt': 23, 'grd': 387.502136220015, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '18.0.8969580780515349163336915861800987000000000000.1', 'local_algs': ['2.2.3.4a1.1', '2.2.3.4a1.1', '2.2.3.4a1.1', '3.1.18.39c2.65', '5.2.3.4a1.1', '5.2.3.4a1.1', '5.2.3.4a1.1', '19.1.3.2a1.3', '19.1.3.2a1.3', '19.1.3.2a1.3', '19.1.3.2a1.3', '19.1.3.2a1.3', '19.1.3.2a1.3'], 'maximal_cm_subfield': [1, -1, 1], 'minimal_sibling': [2750600349, 8011432251, 7962223293, 2437342002, -546767253, -190141911, 129192813, 27041769, -2416230, 1015740, -127413, 44631, 29385, -3591, 1593, -171, 63, 0, 1], 'monogenic': -1, 'narrow_class_group': [3, 3, 3, 3, 6, 18], 'narrow_class_number': 8748, 'num_ram': 4, 'r2': 9, 'ramps': [2, 3, 5, 19], 'rd': 357.216726122, 'regulator': {'__RealLiteral__': 0, 'data': '4411949748464.114', 'prec': 57}, 'subfield_mults': [1, 3, 1, 1, 1, 1], 'subfields': ['1.-1.1', '-171.0.0.1', '2707500.0.0.-2850.0.0.1', '433200.0.0.-1140.0.0.1', '400.0.0.-20.0.0.1', '1083.0.0.0.0.0.1'], 'torsion_gen': '\\( -\\frac{1}{73689288} a^{15} + \\frac{545}{663203592} a^{12} + \\frac{63995}{165800898} a^{9} - 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1/324*a^2 - 1/324*a - 1/324', '1/326916*a^12 + 779/326916*a^9 + 2501/108972*a^6 - 33007/326916*a^3 + 13471/81729', '1/980748*a^13 - 1/980748*a^12 + 779/980748*a^10 - 779/980748*a^9 - 3553/326916*a^7 + 3553/326916*a^6 + 112289/980748*a^4 - 112289/980748*a^3 - 36625/490374*a + 36625/490374', '1/980748*a^14 - 1/980748*a^12 + 779/980748*a^11 - 779/980748*a^9 + 2501/326916*a^8 + 1/54*a^7 - 8555/326916*a^6 + 75965/980748*a^5 - 1/27*a^4 - 39641/980748*a^3 - 13772/245187*a^2 + 1/54*a + 18463/490374', '1/15656247196344*a^15 - 12003005/15656247196344*a^12 - 1228492240/1957030899543*a^9 + 47756813059/1957030899543*a^6 + 1004126499191/15656247196344*a^3 + 2642949232301/15656247196344', '1/16110278365037976*a^16 - 1/46968741589032*a^15 - 7674520445/16110278365037976*a^13 + 59893739/46968741589032*a^12 - 1757259871387/8055139182518988*a^10 + 48025017881/11742185397258*a^9 - 80524949700677/8055139182518988*a^7 - 114406520681/11742185397258*a^6 + 381345295989293/16110278365037976*a^4 - 7368709266323/46968741589032*a^3 - 295286695812985/16110278365037976*a + 5011378892185/46968741589032', '1/5525825479208025768*a^17 - 1/46968741589032*a^15 + 912210698227/5525825479208025768*a^14 - 35887729/46968741589032*a^12 - 2278785279998065/2762912739604012884*a^11 - 1/324*a^10 - 13739471933/23484370794516*a^9 - 806314387232885/2762912739604012884*a^8 - 1/108*a^7 + 64206414617/23484370794516*a^6 + 451835352393214649/5525825479208025768*a^5 + 1/36*a^4 - 1162980063869/46968741589032*a^3 + 2448708823190296007/5525825479208025768*a^2 - 5/324*a - 4353702032249/46968741589032']}
Number field data - 18.0.8969580780515349163336915861800987000000000000.1