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nf_fields • Show schema
{'class_group': [2, 2], 'class_number': 4, 'cm': False, 'coeffs': [1189, -957, 1379, -1020, 1020, -822, 667, -426, 225, -90, 29, -6, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 6775409390765625, 'disc_rad': 435, 'disc_sign': 1, 'frobs': [[2, [[6, 2]]], [3, [0]], [5, [0]], [7, [[6, 2]]], [11, [[3, 4]]], [13, [[6, 2]]], [17, [[6, 2]]], [19, [[2, 6]]], [23, [[2, 6]]], [29, [0]], [31, [[2, 6]]], [37, [[2, 6]]], [41, [[1, 12]]], [43, [[2, 6]]], [47, [[6, 2]]], [53, [[2, 6]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 6, 6], 'galois_label': '12T3', 'galt': 3, 'grd': 20.85665361461421, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': False, 'iso_number': 3, 'label': '12.0.6775409390765625.3', 'local_algs': ['3.4.2.1', '3.4.2.1', '3.4.2.1', '5.4.2.1', '5.4.2.1', '5.4.2.1', '29.2.1.2', '29.2.1.2', '29.2.1.2', '29.2.1.2', '29.2.1.2', '29.2.1.2'], 'minimal_sibling': [-1, 2, 7, 6, 5, -1, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 6, 'ramps': [3, 5, 29], 'rd': 20.8566536146, 'regulator': {'__RealLiteral__': 0, 'data': '217.33692993', 'prec': 40}, 'res': {'sib': ['-1,2,7,6,5,-1,1', '151,91,36,-1,15,-2,1']}, 'subfield_mults': [1, 1, 1, 3, 1, 1, 3, 3], 'subfields': ['22.-1.1', '-1.-1.1', '109.-1.1', '1.2.-1.1', '529.0.41.0.1', '9.-9.30.-9.4.-2.1', '-1.2.7.6.5.-1.1', '151.91.36.-1.15.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1936}{872689} a^{11} - \\frac{10648}{872689} a^{10} + \\frac{46826}{872689} a^{9} - \\frac{130857}{872689} a^{8} + \\frac{267326}{872689} a^{7} - \\frac{399511}{872689} a^{6} + \\frac{413575}{872689} a^{5} - \\frac{287253}{872689} a^{4} + \\frac{496099}{872689} a^{3} - \\frac{585385}{872689} a^{2} + \\frac{48749}{45931} a + \\frac{67175}{872689} \\)', '\\( \\frac{175100}{498305419} a^{11} - \\frac{1160753}{498305419} a^{10} + \\frac{8270855}{498305419} a^{9} - \\frac{26929579}{498305419} a^{8} + \\frac{77711925}{498305419} a^{7} - \\frac{134485292}{498305419} a^{6} + \\frac{198607131}{498305419} a^{5} - \\frac{185869455}{498305419} a^{4} + \\frac{186442882}{498305419} a^{3} - \\frac{140811288}{498305419} a^{2} + \\frac{301014028}{498305419} a - \\frac{89315146}{498305419} \\)', '\\( \\frac{678620}{498305419} a^{11} - \\frac{4075894}{498305419} a^{10} + \\frac{19411375}{498305419} a^{9} - \\frac{56547335}{498305419} a^{8} + \\frac{131627998}{498305419} a^{7} - \\frac{222541228}{498305419} a^{6} + \\frac{281798416}{498305419} a^{5} - \\frac{287249240}{498305419} a^{4} + \\frac{12045030}{21665453} a^{3} - \\frac{318461904}{498305419} a^{2} + \\frac{738776827}{498305419} a - \\frac{156874968}{498305419} \\)', '\\( \\frac{179274}{498305419} a^{11} - \\frac{1183710}{498305419} a^{10} + \\frac{5200200}{498305419} a^{9} - \\frac{12939454}{498305419} a^{8} + \\frac{30699681}{498305419} a^{7} - \\frac{35390387}{498305419} a^{6} + \\frac{81006922}{498305419} a^{5} - \\frac{106847785}{498305419} a^{4} + \\frac{249901617}{498305419} a^{3} - \\frac{523987503}{498305419} a^{2} + \\frac{192748342}{498305419} a - \\frac{634984096}{498305419} \\)', '\\( \\frac{1361414}{498305419} a^{11} - \\frac{8174745}{498305419} a^{10} + \\frac{35752095}{498305419} a^{9} - \\frac{99104545}{498305419} a^{8} + \\frac{216243752}{498305419} a^{7} - \\frac{15042937}{21665453} a^{6} + \\frac{445996623}{498305419} a^{5} - \\frac{21542470}{21665453} a^{4} + \\frac{32501585}{26226601} a^{3} - \\frac{521794604}{498305419} a^{2} + \\frac{870982549}{498305419} a - \\frac{361113467}{498305419} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/249527*a^10 - 5/249527*a^9 - 100812/249527*a^8 - 95776/249527*a^7 - 97172/249527*a^6 - 121870/249527*a^5 - 111647/249527*a^4 + 65155/249527*a^3 - 56119/249527*a^2 + 19191/249527*a + 62748/249527', '1/498305419*a^11 + 993/498305419*a^10 + 52045341/498305419*a^9 - 85734532/498305419*a^8 - 227681403/498305419*a^7 - 36713992/498305419*a^6 - 123983650/498305419*a^5 + 193563443/498305419*a^4 + 194722611/498305419*a^3 - 120116010/498305419*a^2 - 206856096/498305419*a + 243030525/498305419']}
Number field data - 12.0.6775409390765625.3