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{'class_group': [2, 2], 'class_number': 4, 'cm': False, 'coeffs': [64, -128, 208, -176, 32, 64, -88, 32, 8, -22, 13, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1123021498208518144, 'disc_rad': 34, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[12, 1]]], [5, [[8, 1], [4, 1]]], [7, [[8, 1], [4, 1]]], [11, [[12, 1]]], [13, [[4, 1], [3, 2], [1, 2]]], [17, [0]], [19, [[2, 4], [1, 4]]], [23, [[8, 1], [4, 1]]], [29, [[8, 1], [4, 1]]], [31, [[4, 2], [2, 2]]], [37, [[4, 2], [2, 2]]], [41, [[12, 1]]], [43, [[6, 2]]], [47, [[4, 1], [2, 2], [1, 4]]], [53, [[4, 1], [2, 2], [1, 4]]], [59, [[6, 1], [2, 1], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4800, 2112], 'galois_label': '12T238', 'galt': 238, 'grd': 56.89280357730381, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 5, 'label': '12.2.1123021498208518144.5', 'local_algs': ['2.2.3.3', '2.2.3.4', '2.2.3.4', '2.6.6.7', '17.12.11.2'], 'minimal_sibling': [-16, -48, -32, 64, -32, 28, 28, 6, 19, -13, 2, -3, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 5, 'ramps': [2, 17], 'rd': 31.9300064187, 'regulator': {'__RealLiteral__': 0, 'data': '52217.0172233', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-4.-1.1', '-2.4.8.-13.-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{7}{64} a^{11} - \\frac{225}{608} a^{10} + \\frac{1333}{1216} a^{9} - \\frac{429}{304} a^{8} - \\frac{137}{152} a^{7} + \\frac{607}{152} a^{6} - \\frac{913}{152} a^{5} - \\frac{5}{19} a^{4} + \\frac{281}{38} a^{3} - \\frac{953}{76} a^{2} + \\frac{687}{76} a - \\frac{13}{38} \\)', '\\( \\frac{49}{1216} a^{11} - \\frac{135}{608} a^{10} + \\frac{825}{1216} a^{9} - \\frac{191}{152} a^{8} + \\frac{71}{152} a^{7} + \\frac{413}{152} a^{6} - \\frac{789}{152} a^{5} + \\frac{169}{76} a^{4} + \\frac{96}{19} a^{3} - \\frac{669}{76} a^{2} + \\frac{535}{76} a - \\frac{7}{2} \\)', '\\( \\frac{17}{608} a^{11} - \\frac{9}{152} a^{10} + \\frac{89}{608} a^{9} + \\frac{7}{304} a^{8} - \\frac{111}{152} a^{7} + \\frac{101}{152} a^{6} + \\frac{4}{19} a^{5} - \\frac{173}{76} a^{4} + \\frac{35}{38} a^{3} + \\frac{13}{19} a^{2} - \\frac{31}{38} a + \\frac{22}{19} \\)', '\\( \\frac{33}{608} a^{11} - \\frac{63}{304} a^{10} + \\frac{385}{608} a^{9} - \\frac{139}{152} a^{8} - \\frac{15}{76} a^{7} + \\frac{369}{152} a^{6} - \\frac{315}{76} a^{5} + \\frac{13}{38} a^{4} + \\frac{183}{38} a^{3} - \\frac{158}{19} a^{2} + \\frac{161}{38} a - 2 \\)', '\\( \\frac{29}{304} a^{11} - \\frac{45}{152} a^{10} + \\frac{275}{304} a^{9} - \\frac{83}{76} a^{8} - \\frac{127}{152} a^{7} + \\frac{231}{76} a^{6} - \\frac{393}{76} a^{5} + \\frac{5}{38} a^{4} + \\frac{237}{38} a^{3} - \\frac{242}{19} a^{2} + \\frac{134}{19} a - 5 \\)', '\\( \\frac{47}{304} a^{11} - \\frac{143}{304} a^{10} + \\frac{473}{304} a^{9} - \\frac{575}{304} a^{8} - \\frac{47}{76} a^{7} + \\frac{675}{152} a^{6} - \\frac{701}{76} a^{5} + \\frac{11}{19} a^{4} + \\frac{113}{19} a^{3} - \\frac{411}{19} a^{2} + \\frac{196}{19} a - \\frac{181}{19} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a^2', '1/2*a^4 - 1/2*a^2', '1/2*a^5 - 1/2*a^2', '1/4*a^6 - 1/4*a^4', '1/4*a^7 - 1/4*a^5', '1/8*a^8 - 1/8*a^6 - 1/4*a^5 - 1/4*a^4', '1/16*a^9 - 1/16*a^7 - 1/8*a^6 - 1/8*a^5 - 1/4*a^4 - 1/4*a^3 - 1/2*a', '1/304*a^10 - 9/304*a^9 - 1/304*a^8 - 37/304*a^7 + 3/38*a^6 - 7/152*a^5 + 3/19*a^4 + 1/76*a^3 - 1/38*a^2 + 1/38*a + 2/19', '1/1216*a^11 - 1/608*a^10 - 7/1216*a^9 - 11/304*a^8 - 1/19*a^7 + 5/152*a^6 - 11/152*a^5 - 3/19*a^4 + 3/38*a^3 - 3/76*a^2 + 15/76*a + 7/38']}