-
nf_fields • Show schema
{'class_group': [5], 'class_number': 5, 'cm': False, 'coeffs': [-5972, -2624, -7798, -11480, -13117, -3280, -408, -82, 28, 0, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 63580957267604373504, 'disc_rad': 246, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 4], [1, 2]]], [7, [[2, 5]]], [11, [[10, 1]]], [13, [[2, 5]]], [17, [[2, 5]]], [19, [[5, 2]]], [23, [[2, 4], [1, 2]]], [29, [[2, 4], [1, 2]]], [31, [[2, 5]]], [37, [[2, 5]]], [41, [0]], [43, [[5, 2]]], [47, [[2, 4], [1, 2]]], [53, [[2, 4], [1, 2]]], [59, [[2, 5]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [30, 10, 16], 'galois_label': '10T3', 'galt': 3, 'grd': 95.57244712596375, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '10.2.63580957267604373504.1', 'local_algs': ['2.1.2.3a1.2', '2.2.2.6a1.1', '2.2.2.6a1.1', '3.5.2.5a1.2', '41.2.5.8a1.1'], 'minimal_sibling': [687241, 357299, 155917, 42044, 9021, 1115, -139, -56, 17, -1, 1], 'monogenic': -1, 'narrow_class_group': [10], 'narrow_class_number': 10, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 41], 'rd': 95.572447126, 'regulator': {'__RealLiteral__': 0, 'data': '582192.1229160837', 'prec': 57}, 'res': {'gal': ['2621440000,0,-730931200,0,79490576,0,-7116528,0,1133340,0,-190396,0,14381,0,14,0,55,0,-18,0,1'], 'sib': ['687241,357299,155917,42044,9021,1115,-139,-56,17,-1,1', '2621440000,0,-730931200,0,79490576,0,-7116528,0,1133340,0,-190396,0,14381,0,14,0,55,0,-18,0,1']}, 'subfield_mults': [1, 1], 'subfields': ['-6.0.1', '829.431.36.-16.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{82337378}{140434539175} a^{9} - \\frac{1279569}{140434539175} a^{8} + \\frac{2219789121}{140434539175} a^{7} - \\frac{6634764279}{140434539175} a^{6} - \\frac{36255657457}{140434539175} a^{5} - \\frac{259131564829}{140434539175} a^{4} - \\frac{1058428211609}{140434539175} a^{3} - \\frac{684862066358}{140434539175} a^{2} + \\frac{32024120768}{28086907835} a - \\frac{673606233367}{140434539175} \\)', '\\( \\frac{3921704044467}{90477423511383230} a^{9} + \\frac{82385235832957}{90477423511383230} a^{8} - \\frac{151223715500134}{45238711755691615} a^{7} + \\frac{814131272728896}{45238711755691615} a^{6} - \\frac{1224565260975083}{9047742351138323} a^{5} + \\frac{4394139692255352}{45238711755691615} a^{4} - \\frac{32434160833963461}{18095484702276646} a^{3} - \\frac{398374807954427897}{90477423511383230} a^{2} - \\frac{305207014250514454}{45238711755691615} a - \\frac{19433391354663337}{9047742351138323} \\)', '\\( \\frac{3328227561671737}{90477423511383230} a^{9} - \\frac{394640613816131}{90477423511383230} a^{8} + \\frac{45618464620708702}{45238711755691615} a^{7} - \\frac{142452615591031373}{45238711755691615} a^{6} - \\frac{689830460675178829}{45238711755691615} a^{5} - \\frac{5310455448355687863}{45238711755691615} a^{4} - \\frac{41466909574132862791}{90477423511383230} a^{3} - \\frac{26217408696272123387}{90477423511383230} a^{2} + \\frac{727719129274057534}{9047742351138323} a + \\frac{14091755183436415406}{45238711755691615} \\)', '\\( \\frac{334920560229003}{64626731079559450} a^{9} - \\frac{989726826909989}{64626731079559450} a^{8} + \\frac{12746206652319001}{64626731079559450} a^{7} - \\frac{62484952758164799}{64626731079559450} a^{6} + \\frac{42557053367792023}{64626731079559450} a^{5} - \\frac{1263749794441701079}{64626731079559450} a^{4} - \\frac{561817217769155087}{32313365539779725} a^{3} - \\frac{483362262522315204}{32313365539779725} a^{2} - \\frac{4372449850459444}{6462673107955945} a - \\frac{367293969817237431}{32313365539779725} \\)', '\\( \\frac{7057779677911983}{64626731079559450} a^{9} + \\frac{768176723131281}{64626731079559450} a^{8} + \\frac{194498531827857871}{64626731079559450} a^{7} - \\frac{558930118903633229}{64626731079559450} a^{6} - \\frac{3026863644851614437}{64626731079559450} a^{5} - \\frac{23235412098552364519}{64626731079559450} a^{4} - \\frac{46750822373415375272}{32313365539779725} a^{3} - \\frac{39658194690778107644}{32313365539779725} a^{2} - \\frac{286173564707714404}{1292534621591189} a + \\frac{20754362500020385289}{32313365539779725} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/2*a^7 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2', '1/10*a^8 + 1/10*a^7 + 1/10*a^6 + 1/10*a^5 - 1/2*a^4 - 3/10*a^3 + 2/5*a - 2/5', '1/452387117556916150*a^9 + 5810166348474176/226193558778458075*a^8 + 27583402741563957/452387117556916150*a^7 + 32504055259266557/452387117556916150*a^6 + 213971111871756831/452387117556916150*a^5 + 102915027709161807/452387117556916150*a^4 - 42187956805946489/226193558778458075*a^3 + 131652180701777139/452387117556916150*a^2 + 1998649054969178/45238711755691615*a - 44449902097208507/226193558778458075']}
Number field data - 10.2.63580957267604373504.1