LMFDB - Number field search results

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Results (28 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
13.13.50359924122392641.1	$x^{13} - 2 x^{12} - 11 x^{11} + 23 x^{10} + 39 x^{9} - 91 x^{8} - 44 x^{7} + 145 x^{6} - 6 x^{5} - 89 x^{4} + 29 x^{3} + 14 x^{2} - 8 x + 1$	$13$	[13,0]	$50359924122392641$	$1$	$19.2652999174$	$224410169.38274574$		✓	$S_{13}$ (as 13T9)	trivial	$2$	$12$	$8144.93556547$
13.13.74057741281094693.1	$x^{13} - 3 x^{12} - 8 x^{11} + 27 x^{10} + 22 x^{9} - 89 x^{8} - 23 x^{7} + 132 x^{6} + 5 x^{5} - 87 x^{4} + 4 x^{3} + 21 x^{2} - 2 x - 1$	$13$	[13,0]	$74057741281094693$	$1$	$19.8453730138$	$272135520.06508577$		✓	$S_{13}$ (as 13T9)	trivial	$2$	$12$	$10098.9038604$
13.13.491...641.1	$x^{13} - x^{12} - 24 x^{11} + 19 x^{10} + 190 x^{9} - 116 x^{8} - 601 x^{7} + 246 x^{6} + 738 x^{5} - 215 x^{4} - 291 x^{3} + 68 x^{2} + 10 x - 1$	$13$	[13,0]	$53^{12}$	$1$	$39.0516388455$	$39.05163884547241$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$1314145.36669$
13.13.590...441.1	$x^{13} - x^{12} - 36 x^{11} + 77 x^{10} + 365 x^{9} - 1193 x^{8} - 617 x^{7} + 5541 x^{6} - 4414 x^{5} - 4575 x^{4} + 6321 x^{3} + 411 x^{2} - 2196 x + 293$	$13$	[13,0]	$79^{12}$	$1$	$56.4489381067$	$56.44893810672074$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$14045368.3938$
13.13.145...912.1	$x^{13} - 26 x^{11} + 260 x^{9} - 1248 x^{7} + 2912 x^{5} - 2912 x^{3} + 832 x - 176$	$13$	[13,0]	$2^{12}\cdot 7^{6}\cdot 13^{13}$	$3$	$60.5149172415$	$78.14721442881216$		?	$F_{13}$ (as 13T6)	trivial	$2$	$12$	$87393029.0991$
13.13.282...601.1	$x^{13} - 3 x^{12} - 41 x^{11} + 155 x^{10} + 376 x^{9} - 2028 x^{8} - 13 x^{7} + 8927 x^{6} - 7711 x^{5} - 13367 x^{4} + 20364 x^{3} + 1404 x^{2} - 13408 x + 5312$	$13$	[13,0]	$8101^{6}$	$1$	$63.6708880391$	$90.00555538409837$			$D_{13}$ (as 13T2)	trivial	$2$	$12$	$235421273.11$
13.13.353...881.1	$x^{13} - 39 x^{11} + 507 x^{9} - 156 x^{8} - 2925 x^{7} + 1872 x^{6} + 7605 x^{5} - 7488 x^{4} - 6435 x^{3} + 10062 x^{2} - 2691 x - 306$	$13$	[13,0]	$3^{12}\cdot 13^{16}$	$2$	$64.7778937113$	$73.88429313471292$			$C_{13}:C_3$ (as 13T3)	trivial	$2$	$12$	$166789217.838$
13.13.361...641.1	$x^{13} - x^{12} - 50 x^{11} + 25 x^{10} + 722 x^{9} - 226 x^{8} - 4207 x^{7} + 1158 x^{6} + 10465 x^{5} - 2535 x^{4} - 9399 x^{3} + 1079 x^{2} + 1316 x - 49$	$13$	[13,0]	$23^{6}\cdot 367^{6}$	$2$	$64.8906015414$	$91.87491496594704$			$D_{13}$ (as 13T2)	trivial	$2$	$12$	$100827679.942$
13.13.255...961.1	$x^{13} - x^{12} - 60 x^{11} + 27 x^{10} + 1199 x^{9} - 33 x^{8} - 9610 x^{7} - 3352 x^{6} + 33548 x^{5} + 20328 x^{4} - 47723 x^{3} - 34869 x^{2} + 21271 x + 15667$	$13$	[13,0]	$131^{12}$	$1$	$90.0335289186$	$90.03352891861981$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$292369424.433$
13.13.224...601.1	$x^{13} - x^{12} - 72 x^{11} + 129 x^{10} + 1672 x^{9} - 3386 x^{8} - 16810 x^{7} + 32367 x^{6} + 81708 x^{5} - 121902 x^{4} - 196272 x^{3} + 127412 x^{2} + 217458 x + 61399$	$13$	[13,0]	$157^{12}$	$1$	$106.410453613$	$106.41045361273743$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$1334709178.87$
13.13.302...000.1	$x^{13} - 65 x^{11} + 1625 x^{9} - 19500 x^{7} + 113750 x^{5} - 284375 x^{3} + 203125 x - 69500$	$13$	[13,0]	$2^{12}\cdot 5^{12}\cdot 13^{13}$	$3$	$108.898093209$	$137.63336134966406$		?	$F_{13}$ (as 13T6)	trivial	$2$	$12$	$4111386187.29$
13.13.542...361.1	$x^{13} - 78 x^{11} - 65 x^{10} + 2080 x^{9} + 2457 x^{8} - 24128 x^{7} - 27027 x^{6} + 137683 x^{5} + 110214 x^{4} - 376064 x^{3} - 128206 x^{2} + 363883 x - 12167$	$13$	[13,0]	$13^{24}$	$1$	$113.896611641$	$113.89661164093096$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$2733056590.62$
13.13.910...125.1	$x^{13} - 130 x^{11} - 390 x^{10} + 3900 x^{9} + 21255 x^{8} + 10985 x^{7} - 119145 x^{6} - 213785 x^{5} + 106470 x^{4} + 499395 x^{3} + 197730 x^{2} - 296595 x - 205335$	$13$	[13,0]	$3^{6}\cdot 5^{12}\cdot 13^{15}$	$3$	$141.49208407$	$171.13897383055289$			$C_{13}:C_4$ (as 13T4)	trivial	$2$	$12$	$254843353531$
13.13.567...184.1	$x^{13} - 117 x^{11} - 26 x^{10} + 3692 x^{9} + 2938 x^{8} - 38987 x^{7} - 54314 x^{6} + 137670 x^{5} + 290524 x^{4} - 5824 x^{3} - 298948 x^{2} - 169403 x - 13406$	$13$	[13,0]	$2^{12}\cdot 3^{6}\cdot 13^{20}$	$3$	$162.870584734$	$204.39719270911772$		?	$C_{13}:C_6$ (as 13T5)	trivial	$2$	$12$	$95460081074.3$
13.13.884...681.1	$x^{13} - x^{12} - 144 x^{11} + 161 x^{10} + 6530 x^{9} - 9620 x^{8} - 109398 x^{7} + 196143 x^{6} + 512628 x^{5} - 917970 x^{4} - 650724 x^{3} + 1134730 x^{2} + 253950 x - 409375$	$13$	[13,0]	$313^{12}$	$1$	$201.17749146$	$201.177491460457$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$927977436616.0109$
13.13.170...729.1	$x^{13} - 78 x^{11} + 1989 x^{9} - 1326 x^{8} - 21255 x^{7} + 33813 x^{6} + 68328 x^{5} - 216723 x^{4} + 191178 x^{3} - 51948 x^{2} - 5850 x + 1875$	$13$	[13,0]	$3^{12}\cdot 13^{22}$	$2$	$211.618934626$	$249.4371574945215$		?	$C_{13}:C_6$ (as 13T5)	trivial	$2$	$12$	$394704115709$
13.13.116...853.1	$x^{13} - 91 x^{11} - 26 x^{10} + 2951 x^{9} + 1339 x^{8} - 41431 x^{7} - 25922 x^{6} + 234988 x^{5} + 213772 x^{4} - 406770 x^{3} - 373113 x^{2} + 223587 x + 170991$	$13$	[13,0]	$13^{21}\cdot 19^{6}$	$2$	$245.268019027$	$318.4855383265108$			$C_{13}:C_4$ (as 13T4)	trivial	$2$	$12$	$2019070466020$
13.13.571...001.1	$x^{13} - x^{12} - 204 x^{11} - 181 x^{10} + 10752 x^{9} + 9116 x^{8} - 208418 x^{7} - 161679 x^{6} + 1686466 x^{5} + 1207646 x^{4} - 4904338 x^{3} - 3051848 x^{2} + 896956 x + 144209$	$13$	[13,0]	$443^{12}$	$1$	$277.226159648$	$277.22615964805635$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$983737918371.0616$
13.13.362...424.1	$x^{13} - 214 x^{11} - 528 x^{10} + 15084 x^{9} + 63024 x^{8} - 390420 x^{7} - 2357568 x^{6} + 2053638 x^{5} + 30420288 x^{4} + 30740796 x^{3} - 108639936 x^{2} - 240370524 x - 132080544$	$13$	[13,0]	$2^{36}\cdot 3^{16}\cdot 13^{6}\cdot 71^{4}$	$4$	$319.590116921$	$3812.4191094944044$			$\PSL(3,3)$ (as 13T7)	trivial	$2$	$12$	$95129277252200$
13.13.362...424.2	$x^{13} - 222 x^{11} - 64 x^{10} + 18444 x^{9} + 14832 x^{8} - 723404 x^{7} - 1021200 x^{6} + 13437870 x^{5} + 27216624 x^{4} - 96770628 x^{3} - 257555808 x^{2} + 34006548 x + 256489920$	$13$	[13,0]	$2^{36}\cdot 3^{16}\cdot 13^{6}\cdot 71^{4}$	$4$	$319.590116921$	$3812.4191094944044$			$\PSL(3,3)$ (as 13T7)	trivial	$2$	$12$	$95129277252200$
13.13.399...641.1	$x^{13} - x^{12} - 240 x^{11} - 293 x^{10} + 19153 x^{9} + 45777 x^{8} - 616830 x^{7} - 1795569 x^{6} + 7791196 x^{5} + 23224049 x^{4} - 29107980 x^{3} - 68466088 x^{2} + 31673025 x + 4516075$	$13$	[13,0]	$521^{12}$	$1$	$321.995799388$	$321.99579938787$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$15429359577074.87$
13.13.717...241.1	$x^{13} - x^{12} - 252 x^{11} + 1123 x^{10} + 15626 x^{9} - 107844 x^{8} - 204415 x^{7} + 3094114 x^{6} - 4853400 x^{5} - 22393129 x^{4} + 91453411 x^{3} - 116380476 x^{2} + 47088126 x - 1165671$	$13$	[13,0]	$547^{12}$	$1$	$336.800646612$	$336.80064661199583$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$468882596177901.8$
13.13.213...801.1	$x^{13} - x^{12} - 276 x^{11} + 1967 x^{10} + 8169 x^{9} - 109375 x^{8} + 114077 x^{7} + 1684091 x^{6} - 4924742 x^{5} - 5465967 x^{4} + 34969245 x^{3} - 20502539 x^{2} - 55304818 x + 57031547$	$13$	[13,0]	$599^{12}$	$1$	$366.250819642$	$366.25081964246385$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$1689788670896.741$
13.13.926...521.1	$x^{13} - x^{12} - 312 x^{11} + 765 x^{10} + 31073 x^{9} - 114643 x^{8} - 1071164 x^{7} + 4472586 x^{6} + 13888428 x^{5} - 61633266 x^{4} - 43862553 x^{3} + 238916059 x^{2} - 140970591 x - 1052321$	$13$	[13,0]	$677^{12}$	$1$	$410.063466568$	$410.06346656832307$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$3454123871256.3633$
13.13.161...281.1	$x^{13} - x^{12} - 396 x^{11} + 1235 x^{10} + 45719 x^{9} - 158783 x^{8} - 2232951 x^{7} + 7665285 x^{6} + 47857178 x^{5} - 162308625 x^{4} - 381260855 x^{3} + 1359880245 x^{2} + 391778734 x - 2211739517$	$13$	[13,0]	$859^{12}$	$1$	$510.859391801$	$510.85939180125763$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$107792443172161.95$
13.13.326...521.1	$x^{13} - x^{12} - 420 x^{11} + 4253 x^{10} + 2721 x^{9} - 193733 x^{8} + 735262 x^{7} + 31458 x^{6} - 3569396 x^{5} + 1482536 x^{4} + 4833237 x^{3} + 1733969 x^{2} - 40719 x - 57869$	$13$	[13,0]	$911^{12}$	$1$	$539.340604042$	$539.3406040422938$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$345319680754792.2$
13.13.458...681.1	$x^{13} - x^{12} - 432 x^{11} + 1203 x^{10} + 46006 x^{9} - 37046 x^{8} - 2039413 x^{7} - 3276218 x^{6} + 27799988 x^{5} + 87214801 x^{4} - 38878963 x^{3} - 420910202 x^{2} - 520002704 x - 190078187$	$13$	[13,0]	$937^{12}$	$1$	$553.533918196$	$553.5339181962555$	✓		$C_{13}$ (as 13T1)	trivial	$2$	$12$	$169264238822310.44$
13.13.308...625.1	$x^{13} - 2 x^{12} - 306 x^{11} + 737 x^{10} + 35420 x^{9} - 94473 x^{8} - 1919784 x^{7} + 5276958 x^{6} + 48766779 x^{5} - 126847180 x^{4} - 502327474 x^{3} + 1061716068 x^{2} + 1350962689 x - 1362894158$	$13$	[13,0]	$3^{28}\cdot 5^{18}\cdot 29^{12}$	$3$	$2214.91082149$	$16854.804228764082$		?	$A_{13}$ (as 13T8)	trivial	$2$	$12$	$4344433704670000000$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.