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nf_fields • Show schema
{'class_group': [2, 2, 4], 'class_number': 16, 'cm': False, 'coeffs': [718836830208, 0, -59903069184, 0, 1835265600, 0, -26655048, 0, 197064, 0, -714, 0, 1], 'conductor': 2856, 'degree': 12, 'dirichlet_group': [1, 965, 1781, 2209, 1801, 2189, 1517, 2041, 1109, 1633, 169, 293], 'disc_abs': 6401594233356076787154812928, 'disc_rad': 714, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[12, 1]]], [7, [0]], [11, [[12, 1]]], [13, [[1, 12]]], [17, [0]], [19, [[6, 2]]], [23, [[12, 1]]], [29, [[4, 3]]], [31, [[12, 1]]], [37, [[12, 1]]], [41, [[4, 3]]], [43, [[1, 12]]], [47, [[3, 4]]], [53, [[6, 2]]], [59, [[3, 4]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [18, 6, 10, 9], 'galois_label': '12T1', 'galt': 1, 'grd': 207.58247157811073, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.12.6401594233356076787154812928.1', 'local_algs': ['2.6.9.1', '2.6.9.1', '3.12.6.1', '7.12.10.5', '17.12.9.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 0, 'ramps': [2, 3, 7, 17], 'rd': 207.582471578, 'regulator': {'__RealLiteral__': 0, 'data': '1441606350.4875915', 'prec': 60}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-4.-1.1', '1.-2.-1.1', '119952.0.-714.0.1', '-13.-25.57.11.-17.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{409002048} a^{10} - \\frac{61}{45444672} a^{8} + \\frac{49}{190944} a^{6} - \\frac{167}{7956} a^{4} + \\frac{233}{312} a^{2} - \\frac{151}{13} \\)', '\\( \\frac{5}{1090672128} a^{10} - \\frac{1457}{545336064} a^{8} + \\frac{71}{127296} a^{6} - \\frac{2177}{42432} a^{4} + \\frac{209}{104} a^{2} - \\frac{327}{13} \\)', '\\( \\frac{23}{3272016384} a^{10} - \\frac{695}{181778688} a^{8} + \\frac{71}{99008} a^{6} - \\frac{419}{7488} a^{4} + \\frac{87}{52} a^{2} - \\frac{153}{13} \\)', '\\( \\frac{1}{3272016384} a^{10} - \\frac{215}{545336064} a^{8} + \\frac{401}{2673216} a^{6} - \\frac{991}{42432} a^{4} + \\frac{463}{312} a^{2} - \\frac{352}{13} \\)', '\\( \\frac{1}{1636008192} a^{10} - \\frac{5}{16039296} a^{8} + \\frac{25}{668304} a^{6} + \\frac{199}{63648} a^{4} - \\frac{77}{104} a^{2} + \\frac{336}{13} \\)', '\\( \\frac{59}{6544032768} a^{11} - \\frac{1}{25562628} a^{10} - \\frac{839}{155810304} a^{9} + \\frac{5}{250614} a^{8} + \\frac{895}{763776} a^{7} - \\frac{139}{41769} a^{6} - \\frac{1735}{14976} a^{5} + \\frac{8}{39} a^{4} + \\frac{1601}{312} a^{3} - \\frac{128}{39} a^{2} - \\frac{2009}{26} a - \\frac{67}{13} \\)', '\\( \\frac{31}{6544032768} a^{11} - \\frac{1}{25562628} a^{10} - \\frac{991}{363557376} a^{9} + \\frac{5}{250614} a^{8} + \\frac{145}{254592} a^{7} - \\frac{139}{41769} a^{6} - \\frac{827}{14976} a^{5} + \\frac{8}{39} a^{4} + \\frac{271}{104} a^{3} - \\frac{128}{39} a^{2} - \\frac{1253}{26} a - \\frac{613}{13} \\)', '\\( \\frac{737}{3272016384} a^{11} - \\frac{8773}{3272016384} a^{10} - \\frac{3331}{25968384} a^{9} + \\frac{834079}{545336064} a^{8} + \\frac{22991}{891072} a^{7} - \\frac{48439}{157248} a^{6} - \\frac{287693}{127296} a^{5} + \\frac{202217}{7488} a^{4} + \\frac{26605}{312} a^{3} - \\frac{158995}{156} a^{2} - \\frac{14517}{13} a + \\frac{173457}{13} \\)', '\\( \\frac{83}{818004096} a^{11} + \\frac{6073}{3272016384} a^{10} - \\frac{15}{210392} a^{9} - \\frac{683983}{545336064} a^{8} + \\frac{25577}{1336608} a^{7} + \\frac{850937}{2673216} a^{6} - \\frac{78071}{31824} a^{5} - \\frac{4785461}{127296} a^{4} + \\frac{15597}{104} a^{3} + \\frac{632063}{312} a^{2} - \\frac{90793}{26} a - \\frac{498162}{13} \\)', '\\( \\frac{4909}{6544032768} a^{11} + \\frac{14831}{1636008192} a^{10} - \\frac{17177}{40395264} a^{9} - \\frac{200393}{38952576} a^{8} + \\frac{455881}{5346432} a^{7} + \\frac{172517}{167076} a^{6} - \\frac{1897097}{254592} a^{5} - \\frac{338119}{3744} a^{4} + \\frac{175057}{624} a^{3} + \\frac{1061561}{312} a^{2} - \\frac{95311}{26} a - \\frac{578249}{13} \\)', '\\( \\frac{415}{818004096} a^{11} - \\frac{2381}{363557376} a^{10} - \\frac{6319}{22722336} a^{9} + \\frac{93671}{25968384} a^{8} + \\frac{71465}{1336608} a^{7} - \\frac{622103}{891072} a^{6} - \\frac{142445}{31824} a^{5} + \\frac{7498705}{127296} a^{4} + \\frac{50941}{312} a^{3} - \\frac{224805}{104} a^{2} - \\frac{27179}{13} a + \\frac{361106}{13} \\)'], 'used_grh': True, 'zk': ['1', 'a', '1/6*a^2', '1/6*a^3', '1/612*a^4', '1/612*a^5', '1/25704*a^6', '1/51408*a^7 - 1/1224*a^5 - 1/2*a', '1/10487232*a^8 + 1/102816*a^6 - 1/1224*a^4 - 1/24*a^2', '1/20974464*a^9 + 1/205632*a^7 - 1/2448*a^5 + 1/16*a^3 - 1/2*a', '1/3272016384*a^10 - 1/77905152*a^8 - 5/891072*a^6 - 61/127296*a^4 - 5/312*a^2 - 1/13', '1/6544032768*a^11 - 1/155810304*a^9 - 5/1782144*a^7 - 61/254592*a^5 - 5/624*a^3 - 1/26*a']}
Number field data - 12.12.6401594233356076787154812928.1