Number field search results

Results (1-50 of 312 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
13.1.1325925503633.1	x^13 - x^12 - x^11 + x^10 + 3x^8 - x^7 - 5x^6 + x^5 + 4x^4 + 2x^3 - 3x^2 - x + 1	$13$	[1,6]	$97\cdot 13669335089$	$2$	$8.56054611437$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$3.1288056301$
13.1.1346252740661.1	x^13 - 4x^11 + 5x^9 - x^7 - x^6 - x^5 + 2x^4 + 2x^3 - x^2 - 2x + 1	$13$	[1,6]	$1346252740661$	$1$	$8.57057063416$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$3.16017709574$
13.1.1452927822421.1	x^13 - 4x^12 + 6x^11 - x^10 - 10x^9 + 17x^8 - 9x^7 - 9x^6 + 19x^5 - 11x^4 - 2x^3 + 7x^2 - 4x + 1	$13$	[1,6]	$83\cdot 17505154487$	$2$	$8.62099183688$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$3.3104562037$
13.1.3518110599125.1	x^13 + x^11 - 2x^10 + x^9 - x^8 - 4x^7 + 4x^6 - 5x^5 + x^4 + 2x^3 - 4x^2 + 2x - 1	$13$	[1,6]	$5^{3}\cdot 5351\cdot 5259743$	$3$	$9.22785432352$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$6.17827465513$
13.1.4082190012125.1	x^13 - x^12 - 2x^11 + x^10 + 2x^8 + 2x^7 - x^6 - 2x^5 - x^4 + 2x^3 + 2x^2 - 3x + 1	$13$	[1,6]	$5^{3}\cdot 73\cdot 447363289$	$3$	$9.33401960871$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$6.75913142567$
13.3.5570916369223.1	x^13 - x^12 + x^11 - 4x^10 + 5x^9 - 5x^8 + 6x^7 - 2x^6 - 5x^5 + 5x^4 - 7x^3 + 5x^2 - x + 1	$13$	[3,5]	$-\,5570916369223$	$1$	$9.55995604118$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$9.61638823677$
13.3.5717814639679.1	x^13 - 2x^12 - 3x^11 + 7x^10 + 3x^9 - 7x^8 - 6x^7 + 4x^6 + 8x^5 - 3x^4 - 4x^3 + 2x^2 - 1	$13$	[3,5]	$-\,89\cdot 107\cdot 283\cdot 2121631$	$4$	$9.5791150674$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$9.76540201266$
13.3.6855574490939.1	x^13 - x^12 + 2x^11 + 2x^10 - 3x^9 + x^8 - x^7 - 8x^6 - 7x^5 - 6x^4 - 6x^3 - 6x^2 - 4x - 1	$13$	[3,5]	$-\,1798333\cdot 3812183$	$2$	$9.71377386112$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$10.9027200388$
13.3.7805208559959.1	x^13 - 4x^12 + 6x^11 - 6x^10 + 7x^9 - 5x^8 - x^7 + x^6 + 5x^5 - 2x^4 - 3x^3 - x^2 + 1	$13$	[3,5]	$-\,3^{3}\cdot 31\cdot 71\cdot 821\cdot 159977$	$5$	$9.81119450388$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$11.7783503996$
13.3.9197165262683.1	x^13 - 2x^10 + 2x^9 - x^8 - 3x^7 - 3x^6 + 9x^5 - 10x^4 + 7x^3 + 1	$13$	[3,5]	$-\,82163\cdot 111938041$	$2$	$9.93583002049$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$13.0679687985$
13.1.10905397816000.1	x^13 - 3x^12 + 8x^11 - 12x^10 + 15x^9 - 12x^8 + 6x^7 + x^6 - 6x^5 + 8x^4 - 6x^3 + 5x^2 - x + 1	$13$	[1,6]	$2^{6}\cdot 5^{3}\cdot 26141\cdot 52147$	$4$	$10.0668941223$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$12.5128995808$
13.1.12359517706496.1	x^13 - 3x^12 + 5x^11 - 4x^10 + 5x^8 - 7x^7 + 6x^6 - x^5 - 3x^4 + 4x^3 - 2x^2 + 1	$13$	[1,6]	$2^{8}\cdot 71\cdot 5197\cdot 130843$	$4$	$10.1642898312$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$19.8461888915$
13.3.14047799762079.1	x^13 - 2x^12 + 2x^10 - 3x^9 + 4x^8 - 4x^7 + 4x^6 - 5x^5 + 3x^4 - 2x^3 + 3x^2 - x - 1	$13$	[3,5]	$-\,3^{3}\cdot 16103\cdot 32310059$	$3$	$10.2648943838$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$16.6395085824$
13.3.18597951501632.1	x^13 - 2x^12 + x^11 + x^10 - 6x^9 + 3x^8 + 7x^7 - 4x^6 + 4x^4 - 4x^3 - 4x^2 + x + 1	$13$	[3,5]	$-\,2^{6}\cdot 67\cdot 43517\cdot 99667$	$4$	$10.4888550911$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$20.8860106706$
13.3.21982001088443.1	x^13 - x^12 + x^11 + 3x^10 - 8x^9 + 10x^8 - 6x^7 - 5x^6 + 15x^5 - 19x^4 + 15x^3 - 9x^2 + 3x - 1	$13$	[3,5]	$-\,11^{2}\cdot 71\cdot 2558724373$	$3$	$10.6246067266$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$22.4503389791$
13.3.21990353102339.1	x^13 - 2x^12 + 4x^11 - 5x^10 + 3x^9 + x^8 - 4x^7 + 9x^6 - 7x^5 + 2x^4 - 4x^2 + 4x - 1	$13$	[3,5]	$-\,157\cdot 3169\cdot 44198783$	$3$	$10.624917195$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$22.0576155446$
13.1.24777340928000.1	x^13 - 2x^12 + 4x^11 - 5x^10 + 2x^9 + x^8 - 6x^7 + 8x^6 - 3x^5 + 4x^4 + 4x^3 - x^2 + 4x - 1	$13$	[1,6]	$2^{14}\cdot 5^{3}\cdot 12098311$	$3$	$10.7228912075$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$32.3528276422$
13.5.28261626739249.1	x^13 - 3x^12 + 3x^11 + 3x^10 - 13x^9 + 14x^8 + 2x^7 - 20x^6 + 18x^5 + x^4 - 11x^3 + 6x^2 + x - 1	$13$	[5,4]	$2161\cdot 13078031809$	$2$	$10.8319706242$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$8$	$33.0726626498$
13.5.28318356165577.1	x^13 - 3x^11 - 4x^10 + 2x^9 + 9x^8 + 6x^7 - 4x^6 - 10x^5 - 3x^4 + 4x^3 + 4x^2 - 1	$13$	[5,4]	$1721\cdot 16454593937$	$2$	$10.8336416122$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$8$	$33.1184429974$
13.1.29747917088000.1	x^13 - 4x^12 + 10x^11 - 20x^10 + 30x^9 - 40x^8 + 44x^7 - 43x^6 + 38x^5 - 31x^4 + 24x^3 - 16x^2 + 8x - 2	$13$	[1,6]	$2^{8}\cdot 5^{3}\cdot 139\cdot 6687931$	$4$	$10.8747613641$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$36.4190725607$
13.3.34372007159104.1	x^13 - x^12 - 2x^11 + 5x^10 + x^9 - 8x^8 + 5x^7 + 7x^6 - 2x^4 - 4x - 1	$13$	[3,5]	$-\,2^{6}\cdot 29\cdot 239\cdot 77487031$	$4$	$10.9962987482$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$29.7815563037$
13.1.36713824791125.1	x^13 - x^12 + x^10 - x^8 + 4x^5 - 9x^4 + 12x^3 - 8x^2 + 4x - 1	$13$	[1,6]	$5^{3}\cdot 374321\cdot 784649$	$3$	$11.0521923112$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$40.9666710856$
13.1.48103150106125.1	x^13 - 2x^12 + 4x^10 - 3x^9 - 5x^8 + 7x^7 + x^6 - 8x^5 + 3x^4 + 5x^3 - 3x^2 - x + 2	$13$	[1,6]	$5^{3}\cdot 83\cdot 4636448203$	$3$	$11.2843068169$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$47.5944591354$
13.1.48551226272641.1	x^13 - 2x^12 + 4x^10 - 5x^9 + x^8 + 5x^7 - 11x^6 + 19x^5 - 22x^4 + 16x^3 - 10x^2 + 6x - 1	$13$	[1,6]	$191^{6}$	$1$	$11.2923578172$			not computed	$D_{13}$ (as 13T2)	trivial	$2$	$6$	$26.2176148631$
13.3.49047631346319.1	x^13 - 2x^12 + 3x^11 + 2x^10 - 9x^9 + 12x^8 - 2x^7 - 19x^6 + 27x^5 - 19x^4 - x^3 + 11x^2 - 6x + 1	$13$	[3,5]	$-\,3\cdot 16349210448773$	$2$	$11.3011974948$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$44.4479338582$
13.3.53877019237375.1	x^13 - 2x^12 - 4x^11 + 7x^10 + 6x^9 - 6x^8 - 6x^7 - 8x^6 + 8x^5 + 15x^4 - 7x^3 - 7x^2 + x + 1	$13$	[3,5]	$-\,5^{3}\cdot 204793\cdot 2104643$	$3$	$11.3831330569$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$39.9707034173$
13.1.57655000561921.1	x^13 - 3x^12 + 7x^11 - 10x^10 + 15x^9 - 17x^8 + 19x^7 - 18x^6 + 15x^5 - 12x^4 + 6x^3 - 3x^2 + 2x - 1	$13$	[1,6]	$7^{4}\cdot 83^{2}\cdot 1867^{2}$	$3$	$11.4426317504$			not computed	$A_{13}$ (as 13T8)	trivial	$2$	$6$	$43.4347813984$
13.3.60464861374756.1	x^13 - x^11 - 3x^10 - x^9 + 4x^8 + 5x^7 - x^6 - 6x^5 - 5x^4 + x^3 + 4x^2 + 3x + 1	$13$	[3,5]	$-\,2^{2}\cdot 15116215343689$	$2$	$11.4845932957$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$66.5258088388$
13.3.69188908404875.1	x^13 - 3x^12 + 3x^11 - 3x^10 + 5x^9 + 2x^8 - 17x^7 + 10x^6 + 16x^5 - 16x^4 - 5x^3 + 7x^2 - 1	$13$	[3,5]	$-\,5^{3}\cdot 7^{5}\cdot 31\cdot 1062367$	$4$	$11.6042797679$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$49.3240960032$
13.3.96082590998375.1	x^13 - 4x^11 - 3x^10 + 9x^9 + 10x^8 - 4x^7 - 12x^6 - 13x^5 + 5x^4 + 12x^3 - x + 1	$13$	[3,5]	$-\,5^{3}\cdot 768660727987$	$2$	$11.9011260303$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$61.9626233533$
13.3.105628246955776.1	x^13 - x^12 + 3x^11 - x^10 + 3x^9 + 6x^8 - 6x^7 + x^6 + 6x^5 - 8x^4 - 9x^3 + 2x^2 + 4x + 1	$13$	[3,5]	$-\,2^{8}\cdot 257\cdot 1605487703$	$3$	$11.9881539994$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$94.5194105196$
13.3.114312593686528.1	x^13 - x^12 - 5x^11 + 15x^9 + 9x^8 - 28x^7 - 20x^6 + 26x^5 + 20x^4 - 12x^3 - 10x^2 + 2x + 2	$13$	[3,5]	$-\,2^{14}\cdot 6977087017$	$2$	$12.0612370249$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$95.7333582025$
13.5.132939170094109.1	x^13 - x^12 - x^11 - 3x^10 + x^9 + 5x^8 + 5x^7 + 3x^6 - 7x^5 - 7x^4 - 4x^3 + 2x^2 + 4x + 1	$13$	[5,4]	$132939170094109$	$1$	$12.2021074028$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$8$	$84.1149437602$
13.3.134713017952000.1	x^13 - 5x^12 + 15x^11 - 34x^10 + 56x^9 - 79x^8 + 85x^7 - 78x^6 + 53x^5 - 25x^4 + 6x^3 + 4x^2 - 2x + 1	$13$	[3,5]	$-\,2^{8}\cdot 5^{3}\cdot 4209781811$	$3$	$12.214555267$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$115.220069967$
13.7.137400291790087.1	x^13 - 4x^12 + x^11 + 15x^10 - 18x^9 - 15x^8 + 38x^7 - 5x^6 - 32x^5 + 17x^4 + 11x^3 - 10x^2 - x + 1	$13$	[7,3]	$-\,137400291790087$	$1$	$12.2331277739$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$9$	$110.814756768$
13.7.146839998625007.1	x^13 - 2x^11 - 3x^10 - 4x^9 + 7x^8 + 6x^7 - 4x^6 - 2x^5 - 5x^4 + 5x^3 + 3x^2 - 4x + 1	$13$	[7,3]	$-\,146839998625007$	$1$	$12.2958132764$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$9$	$115.283453799$
13.3.156408138976000.1	x^13 - 3x^12 + 3x^11 - 4x^10 + 4x^9 + 7x^8 - 20x^7 + 27x^6 - 35x^5 + 41x^4 - 36x^3 + 24x^2 - 12x + 4	$13$	[3,5]	$-\,2^{8}\cdot 5^{3}\cdot 137\cdot 599\cdot 59561$	$5$	$12.3556644027$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$127.407170199$
13.5.197683647463424.1	x^13 - 2x^12 + x^11 - 3x^10 - 5x^9 + 7x^8 + 2x^7 + 6x^6 + 4x^5 - 6x^4 - 8x^3 + 6x - 2	$13$	[5,4]	$2^{14}\cdot 12065652311$	$2$	$12.5802727589$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$8$	$173.327894786$
13.3.215762905145828.1	x^13 - 2x^12 + x^11 + 5x^10 - 10x^9 + 4x^8 + 8x^7 - 13x^6 + 5x^5 + 10x^4 - 9x^3 - 3x^2 + 4x + 1	$13$	[3,5]	$-\,2^{2}\cdot 953\cdot 10313\cdot 5488313$	$4$	$12.665245094$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$143.677539316$
13.1.293959006143997.1	x^13 - x - 1	$13$	[1,6]	$28201\cdot 10423708597$	$2$	$12.9701541049$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$64.2478498014$
13.1.311791207040509.1	x^13 + x - 1	$13$	[1,6]	$7\cdot 17\cdot 47\cdot 277\cdot 1723\cdot 116803$	$6$	$13.0290456243$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$6$	$117.917198366$
13.1.330928743953809.1	x^13 - 6x^12 + 15x^11 - 21x^10 + 19x^9 - 13x^8 + 12x^7 - 22x^6 + 36x^5 - 38x^4 + 27x^3 - 16x^2 + 8x - 1	$13$	[1,6]	$263^{6}$	$1$	$13.0888850353$			not computed	$D_{13}$ (as 13T2)	trivial	$2$	$6$	$88.0923358606$
13.3.509211272757248.1	x^13 - x^12 - 2x^11 - 2x^10 + 3x^9 + 4x^8 + 8x^7 - 4x^6 - 13x^5 + 3x^4 + 2x^3 - 6x^2 + x + 2	$13$	[3,5]	$-\,2^{14}\cdot 31079789597$	$2$	$13.5300638744$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$379.340811006$
13.9.737652920184769.1	x^13 - 2x^12 - 8x^11 + 17x^10 + 21x^9 - 53x^8 - 19x^7 + 75x^6 - 48x^4 + 5x^3 + 12x^2 - x - 1	$13$	[9,2]	$737652920184769$	$1$	$13.9213364037$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$10$	$394.327696405$
13.9.748906923760081.1	x^13 - x^12 - 8x^11 + 3x^10 + 28x^9 - 50x^7 - 3x^6 + 44x^5 - 4x^4 - 17x^3 + 5x^2 + 2x - 1	$13$	[9,2]	$364027\cdot 2057284003$	$2$	$13.9375602364$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$10$	$397.580907117$
13.5.1204994394291500.1	x^13 - 3x^12 + 2x^10 + 6x^9 - 9x^7 - 3x^6 + x^5 + 4x^4 - 8x^3 - 3x^2 + 3x + 1	$13$	[5,4]	$2^{2}\cdot 5^{3}\cdot 83\cdot 11171\cdot 2599231$	$5$	$14.4569197834$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$8$	$546.676164956$
13.1.1414971204906609.1	x^13 - x^12 + x^11 + x^10 - x^9 + x^8 - x^7 + 4x^5 - 5x^4 + 4x^3 - 2x + 1	$13$	[1,6]	$3^{6}\cdot 7^{2}\cdot 29^{2}\cdot 6863^{2}$	$4$	$14.6366646729$			not computed	$A_{13}$ (as 13T8)	trivial	$2$	$6$	$307.196082794$
13.3.1990387975424000.1	x^13 - x^12 - 4x^11 - 2x^10 + 6x^9 + 3x^8 - x^7 - 6x^6 + x^4 + x^3 - 12x^2 - 3x + 1	$13$	[3,5]	$-\,2^{11}\cdot 5^{3}\cdot 84089\cdot 92461$	$4$	$15.0259301129$			not computed	$S_{13}$ (as 13T9)	trivial	$2$	$7$	$942.961496704$
13.11.4161299413431551.1	x^13 - x^12 - 9x^11 + 5x^10 + 27x^9 - 6x^8 - 29x^7 - 3x^6 + x^5 + 6x^4 + 12x^3 - 4x - 1	$13$	[11,1]	$-\,137\cdot 14653\cdot 29411\cdot 70481$	$4$	$15.9030033771$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$11$	$1435.89972821$
13.11.4712558875285687.1	x^13 - 6x^11 - 3x^10 + 9x^9 + 19x^8 + 7x^7 - 42x^6 - 25x^5 + 39x^4 + 15x^3 - 14x^2 - 2x + 1	$13$	[11,1]	$-\,4712558875285687$	$1$	$16.0559178572$			✓	$S_{13}$ (as 13T9)	trivial	$2$	$11$	$1547.38105528$