-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -18, -22, 50, 62, -17, -69, -100, 172, -7, -87, 51, -17, 7, -4, 1], 'conductor': 0, 'degree': 15, 'disc_abs': 24417546297445042591, 'disc_rad': 31, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [27], 'galois_label': '15T4', 'galt': 4, 'grd': 21.990014941549536, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '15.5.24417546297445042591.1', 'local_algs': ['31.1.5.4a1.1', '31.1.10.9a1.1'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 5, 'ramps': [31], 'rd': 19.61161992504764, 'regulator': {'__RealLiteral__': 0, 'data': '6179.9389969906615', 'prec': 60}, 'subfield_mults': [1, 1], 'subfields': ['-1.1.0.1', '-5.1.21.-12.-1.1'], 'torsion_order': 2, 'used_grh': False} -
nf_fields_extra • Show schema
{'dirichlet_group': [], 'frobs': [[2, [[15, 1]]], [3, [[10, 1], [5, 1]]], [5, [[3, 5]]], [7, [[15, 1]]], [11, [[10, 1], [5, 1]]], [13, [[10, 1], [5, 1]]], [17, [[10, 1], [5, 1]]], [19, [[15, 1]]], [23, [[10, 1], [5, 1]]], [29, [[10, 1], [5, 1]]], [31, [0]], [37, [[2, 5], [1, 5]]], [41, [[15, 1]]], [43, [[10, 1], [5, 1]]], [47, [[5, 3]]], [53, [[10, 1], [5, 1]]], [59, [[15, 1]]]], 'label': '15.5.24417546297445042591.1', 'res': {'gal': ['149,-245,-111,912,-924,-1504,4883,-6410,6458,-6808,7465,-7549,7365,-7555,8879,-6889,6013,-5012,3547,-1516,2135,136,739,182,109,44,-5,5,-4,-1,1']}, 'torsion_gen': '\\( -1 \\)', 'unit_signature_rank': 5, 'units': ['\\( \\frac{243059409}{2328257544133} a^{14} - \\frac{58795611972}{2328257544133} a^{13} + \\frac{283835217917}{2328257544133} a^{12} - \\frac{671174577289}{2328257544133} a^{11} + \\frac{1545391784548}{2328257544133} a^{10} - \\frac{4167500959675}{2328257544133} a^{9} + \\frac{8618200703888}{2328257544133} a^{8} - \\frac{6698796274221}{2328257544133} a^{7} - \\frac{6040944747651}{2328257544133} a^{6} + \\frac{14805483642160}{2328257544133} a^{5} - \\frac{5586924398371}{2328257544133} a^{4} - \\frac{724165140729}{2328257544133} a^{3} - \\frac{5814004335306}{2328257544133} a^{2} + \\frac{4159657329275}{2328257544133} a + \\frac{3685669397498}{2328257544133} \\)', '\\( \\frac{267585097919}{2328257544133} a^{14} - \\frac{1253520182462}{2328257544133} a^{13} + \\frac{2641390360838}{2328257544133} a^{12} - \\frac{6138719447285}{2328257544133} a^{11} + \\frac{17569473744530}{2328257544133} a^{10} - \\frac{34144131166079}{2328257544133} a^{9} + \\frac{18485848976355}{2328257544133} a^{8} + \\frac{36794259919607}{2328257544133} a^{7} - \\frac{47010188618512}{2328257544133} a^{6} + \\frac{9288455272432}{2328257544133} a^{5} - \\frac{14348444844804}{2328257544133} a^{4} + \\frac{23900361256751}{2328257544133} a^{3} + \\frac{6093122570911}{2328257544133} a^{2} - \\frac{4109472049064}{2328257544133} a - \\frac{2536176204826}{2328257544133} \\)', '\\( \\frac{107616096499}{2328257544133} a^{14} - \\frac{279921774352}{2328257544133} a^{13} + \\frac{273579756429}{2328257544133} a^{12} - \\frac{1174327988520}{2328257544133} a^{11} + \\frac{3541136186138}{2328257544133} a^{10} - \\frac{3439217257266}{2328257544133} a^{9} - \\frac{8823909868513}{2328257544133} a^{8} + \\frac{10130838537873}{2328257544133} a^{7} + \\frac{10141573761668}{2328257544133} a^{6} - \\frac{5961882724531}{2328257544133} a^{5} - \\frac{18352065081316}{2328257544133} a^{4} - \\frac{664268199043}{2328257544133} a^{3} + \\frac{11897335245225}{2328257544133} a^{2} + \\frac{3226043066405}{2328257544133} a - \\frac{827874003385}{2328257544133} \\)', '\\( \\frac{15534851802}{2328257544133} a^{14} - \\frac{310420367835}{2328257544133} a^{13} + \\frac{846059759719}{2328257544133} a^{12} - \\frac{1224851620432}{2328257544133} a^{11} + \\frac{4012431435855}{2328257544133} a^{10} - \\frac{10833583530070}{2328257544133} a^{9} + \\frac{11924086802913}{2328257544133} a^{8} + \\frac{16551040214255}{2328257544133} a^{7} - \\frac{28146605200127}{2328257544133} a^{6} - \\frac{9744470481690}{2328257544133} a^{5} + \\frac{11980428858427}{2328257544133} a^{4} + \\frac{27406648660638}{2328257544133} a^{3} - \\frac{1611692855579}{2328257544133} a^{2} - \\frac{13921249553043}{2328257544133} a - \\frac{3308306735870}{2328257544133} \\)', '\\( \\frac{221069717989}{2328257544133} a^{14} - \\frac{812803982821}{2328257544133} a^{13} + \\frac{1441695630178}{2328257544133} a^{12} - \\frac{3830724914016}{2328257544133} a^{11} + \\frac{10919146009939}{2328257544133} a^{10} - \\frac{18122667063096}{2328257544133} a^{9} - \\frac{453458022259}{2328257544133} a^{8} + \\frac{27069382635229}{2328257544133} a^{7} - \\frac{17519724693137}{2328257544133} a^{6} + \\frac{69067802221}{2328257544133} a^{5} - \\frac{13704436043447}{2328257544133} a^{4} + \\frac{4042596563740}{2328257544133} a^{3} + \\frac{4776557664914}{2328257544133} a^{2} + \\frac{1488718191345}{2328257544133} a + \\frac{3046632114016}{2328257544133} \\)', '\\( \\frac{106584952006}{2328257544133} a^{14} - \\frac{459656461286}{2328257544133} a^{13} + \\frac{1012465523189}{2328257544133} a^{12} - \\frac{2613992273846}{2328257544133} a^{11} + \\frac{7131863600067}{2328257544133} a^{10} - \\frac{13756623825798}{2328257544133} a^{9} + \\frac{10104727394380}{2328257544133} a^{8} + \\frac{3923788363950}{2328257544133} a^{7} - \\frac{10441282622150}{2328257544133} a^{6} + \\frac{11823397836943}{2328257544133} a^{5} - \\frac{15073170859941}{2328257544133} a^{4} + \\frac{9596079935112}{2328257544133} a^{3} - \\frac{2226004000257}{2328257544133} a^{2} - \\frac{1474073828694}{2328257544133} a + \\frac{942994534295}{2328257544133} \\)', '\\( \\frac{1151156254397}{2328257544133} a^{14} - \\frac{4823448537837}{2328257544133} a^{13} + \\frac{9134091304009}{2328257544133} a^{12} - \\frac{21865623729734}{2328257544133} a^{11} + \\frac{63766691902375}{2328257544133} a^{10} - \\frac{114734559068094}{2328257544133} a^{9} + \\frac{20949315679253}{2328257544133} a^{8} + \\frac{182877151681740}{2328257544133} a^{7} - \\frac{154002735802108}{2328257544133} a^{6} - \\frac{28038620815650}{2328257544133} a^{5} - \\frac{22617506148656}{2328257544133} a^{4} + \\frac{69907726933390}{2328257544133} a^{3} + \\frac{37427374092455}{2328257544133} a^{2} - \\frac{29479559531629}{2328257544133} a - \\frac{9738854803650}{2328257544133} \\)', '\\( \\frac{1049496746131}{2328257544133} a^{14} - \\frac{4249575155725}{2328257544133} a^{13} + \\frac{8000993702770}{2328257544133} a^{12} - \\frac{19776577180236}{2328257544133} a^{11} + \\frac{56975492704171}{2328257544133} a^{10} - \\frac{100984549198382}{2328257544133} a^{9} + \\frac{17616560734730}{2328257544133} a^{8} + \\frac{148832776558315}{2328257544133} a^{7} - \\frac{123755117658611}{2328257544133} a^{6} - \\frac{8095199139875}{2328257544133} a^{5} - \\frac{37055740357823}{2328257544133} a^{4} + \\frac{49720924501894}{2328257544133} a^{3} + \\frac{27438573459884}{2328257544133} a^{2} - \\frac{17514774224470}{2328257544133} a - \\frac{659456866622}{2328257544133} \\)', '\\( \\frac{292952766669}{2328257544133} a^{14} - \\frac{834149796827}{2328257544133} a^{13} + \\frac{1144564268545}{2328257544133} a^{12} - \\frac{3951254014228}{2328257544133} a^{11} + \\frac{11055772575791}{2328257544133} a^{10} - \\frac{14236867825707}{2328257544133} a^{9} - \\frac{14330025219917}{2328257544133} a^{8} + \\frac{25327746559616}{2328257544133} a^{7} + \\frac{6359205033623}{2328257544133} a^{6} - \\frac{4692446767528}{2328257544133} a^{5} - \\frac{26613128068049}{2328257544133} a^{4} - \\frac{5299438870211}{2328257544133} a^{3} + \\frac{10542446704233}{2328257544133} a^{2} + \\frac{6876427063067}{2328257544133} a + \\frac{1823742076844}{2328257544133} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', '1/67*a^13 - 30/67*a^12 + 15/67*a^11 - 27/67*a^10 + 27/67*a^9 + 22/67*a^8 + 17/67*a^7 + 32/67*a^6 + 14/67*a^5 - 12/67*a^4 + 6/67*a^3 - 9/67*a^2 + 7/67*a - 23/67', '1/2328257544133*a^14 + 16975831322/2328257544133*a^13 + 935820820203/2328257544133*a^12 - 434972844569/2328257544133*a^11 - 814302805997/2328257544133*a^10 - 211932806836/2328257544133*a^9 + 12371814752/2328257544133*a^8 - 357482693880/2328257544133*a^7 - 6663952029/2328257544133*a^6 - 683853589830/2328257544133*a^5 - 1156621051070/2328257544133*a^4 + 132213504029/2328257544133*a^3 - 1154630429440/2328257544133*a^2 - 892730603990/2328257544133*a + 1076347464613/2328257544133']}
Number field data - 15.5.24417546297445042591.1