-
nf_fields • Show schema
{'class_group': [5, 15], 'class_number': 75, 'cm': False, 'coeffs': [43616907, 65659860, 18877630, -21180600, 5715400, -767889, 36285, 0, 205, 0, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 296071904094910125732421875, 'disc_rad': 615, 'disc_sign': -1, 'frobs': [[2, [[10, 1]]], [3, [0]], [5, [0]], [7, [[3, 2], [1, 4]]], [11, [[10, 1]]], [13, [[3, 2], [1, 4]]], [17, [[10, 1]]], [19, [[5, 2]]], [23, [[10, 1]]], [29, [[10, 1]]], [31, [[2, 4], [1, 2]]], [37, [[2, 4], [1, 2]]], [41, [0]], [43, [[5, 2]]], [47, [[6, 1], [2, 2]]], [53, [[10, 1]]], [59, [[10, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [60, 192, 96], 'galois_label': '10T11', 'galt': 11, 'grd': 443.7513830832364, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.0.296071904094910125732421875.1', 'local_algs': ['3.1.2.1a1.1', '3.2.2.2a1.2', '3.2.2.2a1.2', '5.2.5.16a4.5', '41.2.5.8a1.1'], 'maximal_cm_subfield': [1, -1, 1], 'monogenic': 0, 'narrow_class_group': [5, 15], 'narrow_class_number': 75, 'num_ram': 3, 'r2': 5, 'ramps': [3, 5, 41], 'rd': 443.7513830832364, 'regulator': {'__RealLiteral__': 0, 'data': '102270212.80456363', 'prec': 60}, 'res': {'sib': ['-21014242499,10482674995,41898796840,-5626455460,-33389476930,-7646963371,8505111310,4760855470,718633795,-24880615,-13025494,2486885,1518170,-38905,-56815,-2121,570,165,-35,-5,1', '-753743,-854921,-688589,-295700,65920,8118,-13894,3669,-755,65,22,-1,1', '152473104,-1274239512,4841798976,-10798529742,15751968309,-15839711244,11174213007,-5434533306,1704566602,-305527854,58306411,-59947788,47055029,-21055878,5580876,-850353,85559,-27897,14919,-3528,236,-3,4,-3,1', '3486784401,-17433922005,46490458680,-87169610025,127848761370,-156517877556,-77244949350,1061627799240,-3036420039960,5588556497055,-7775556317721,8655699141225,-3474001801530,-16142348673630,52258156239915,-93835740363777,123411731359320,-129315862927710,112142276293635,-82084721882985,51236324648199,-27361573960995,12460252921515,-4789476404730,1523601621720,-386155310139,71684713635,-7381046490,-529492730,439755075,-131679729,31547565,-5713560,665880,-16150,-10908,2970,-675,120,-15,1', '4623772951,-31132380095,90214637320,-146513546605,145292990840,-89594671489,33253620400,-6689863070,583830490,-73153450,43530497,-8794300,-272860,410870,-52225,-411,165,30,-5,-5,1', '658281649,-6038881065,30709453785,-106770824245,281522741895,-593454774408,1034097365900,-1519093452600,1903888710450,-2046396981450,1887916491765,-1488908510850,995659543775,-556044019425,252930715800,-89164919765,21682197450,-2004104925,-955120275,546329025,-149467515,32216800,-5284575,635025,-63400,3042,-45,-245,90,-15,1', '82148964031222443,0,-19498377888299565,0,97915304391885,0,728001720236205,0,-107607218630130,0,4236224873497,0,644305064485,0,-46358363415,0,1305961080,0,114856920,0,13881171,0,2649915,0,103290,0,1770,0,55,0,1', '887364,59346,-59907,-4095,11455,-4974,3304,-663,-30,15,-2,-3,1']}, 'subfield_mults': [1, 1], 'subfields': ['1.-1.1', '68593.14760.-2665.410.0.1'], 'torsion_gen': '\\( \\frac{24633250}{39911933654592393} a^{9} + \\frac{180234785}{1287481730793303} a^{8} + \\frac{27854147230}{39911933654592393} a^{7} + \\frac{13571419985}{429160576931101} a^{6} + \\frac{2075753560613}{13303977884864131} a^{5} + \\frac{1723268669625}{324487265484491} a^{4} - \\frac{77006311085860}{973461796453473} a^{3} + \\frac{464239961384440}{973461796453473} a^{2} - \\frac{1162768760687215}{973461796453473} a - \\frac{5850603705278}{10467331144661} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{546264208245130}{63365988344453993751} a^{9} + \\frac{2465936529775786}{63365988344453993751} a^{8} + \\frac{125438972817106451}{63365988344453993751} a^{7} + \\frac{2197026588996835}{237325799042898853} a^{6} + \\frac{561627072188168585}{1545511910840341311} a^{5} - \\frac{361627697723763240}{73595805278111491} a^{4} + \\frac{2108392376147062973}{73595805278111491} a^{3} - \\frac{108197785126661806843}{1545511910840341311} a^{2} - \\frac{77961245622145481310}{515170636946780437} a - \\frac{45336271560612208934}{515170636946780437} \\)', '\\( \\frac{9713272754935855052137097938}{93540268508479705061} a^{9} + \\frac{27104215678374440604212499302}{63365988344453993751} a^{8} + \\frac{44909625198344331372054087159806}{1964345638678073806281} a^{7} + \\frac{834231662472657508345895332913}{9052284049207713393} a^{6} + \\frac{65363950454257909102382880102083}{15970289745350193547} a^{5} - 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1/3*a', '1/123*a^6 + 1/3*a^4 - 1/3*a^2', '1/123*a^7 - 1/3*a', '1/6053691*a^8 + 12637/6053691*a^7 - 479/288271*a^6 - 998/2017897*a^5 - 10358/49217*a^4 + 6050/49217*a^3 + 42608/147651*a^2 + 6122/147651*a - 14675/49217', '1/1964345638678073806281*a^9 - 62542869266/63365988344453993751*a^8 - 1282892839339384796/654781879559357935427*a^7 + 214799515317181189/63365988344453993751*a^6 - 34519901571266185/93540268508479705061*a^5 - 19095518813313347465/47910869236050580641*a^4 - 19140359871184326184/47910869236050580641*a^3 - 3769589130231983225/47910869236050580641*a^2 + 6767806333940063686/15970289745350193547*a + 101044799615264201/515170636946780437']}
Number field data - 10.0.296071904094910125732421875.1