Number field search results

Results (1-50 of 197 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
19.1.272...391.1	x^19 - x^18 + 2x^17 - 5x^16 + 8x^15 - 14x^14 + 13x^13 - 10x^12 - x^11 + 9x^10 - 18x^9 + 25x^8 - 10x^7 - 4x^6 + 38x^5 - 42x^4 + 37x^3 - 16x^2 + 4x + 1	$19$	[1,9]	$-\,311^{9}$	$1$	$15.1628639032$			not computed	$D_{19}$ (as 19T2)	trivial	$2$	$9$	$2166.17030371$
19.1.990...639.1	x^19 - 2x^18 + 2x^17 - 2x^16 - 3x^15 + 14x^14 - 7x^13 - 22x^12 + 30x^11 - 9x^10 + 5x^9 - 2x^8 - 51x^7 + 90x^6 - 19x^5 - 91x^4 + 113x^3 - 59x^2 + 14x - 1	$19$	[1,9]	$-\,359^{9}$	$1$	$16.2296030083$			not computed	$D_{19}$ (as 19T2)	trivial	$2$	$9$	$4771.45184867$
19.1.193...555.1	x^19 - x - 1	$19$	[1,9]	$-\,5\cdot 659\cdot 588489604729898953429$	$3$	$18.9799223948$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$31427.0586812$
19.1.201...403.1	x^19 + x - 1	$19$	[1,9]	$-\,149\cdot 2063\cdot 6564253087266573169$	$3$	$19.0197028269$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$40842.9289744$
19.1.756...064.1	x^19 - 2x^18 + 8x^17 - 12x^16 + 43x^15 - 74x^14 + 108x^13 - 18x^12 - 25x^11 + 338x^9 - 70x^8 - 264x^7 - 128x^6 + 120x^5 + 98x^4 + 43x^3 - 22x^2 - 31x - 8	$19$	[1,9]	$-\,2^{18}\cdot 19^{16}$	$2$	$23.0160848178$			not computed	$F_{19}$ (as 19T6)	trivial	$2$	$9$	$540383.098056$
19.3.146...972.1	x^19 - 2x^18 + 7x^16 - 10x^15 - x^14 + 19x^13 - 19x^12 - 9x^11 + 33x^10 - 19x^9 - 20x^8 + 32x^7 - 9x^6 - 17x^5 + 17x^4 - 3x^3 - 5x^2 + 4x - 1	$19$	[3,8]	$2^{2}\cdot 139\cdot 126311\cdot 1021043\cdot 2043393285469$	$5$	$23.8316032998$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$10$	$737873.586636$
19.1.467...879.1	x^19 - 5x^18 + 10x^17 - 5x^16 + 9x^15 - 42x^14 + 51x^13 - 6x^12 - 23x^11 + 4x^10 - 29x^9 + 112x^8 - 63x^7 - 147x^6 + 183x^5 + 15x^4 - 77x^3 - 17x^2 + 37x + 1	$19$	[1,9]	$-\,919^{9}$	$1$	$25.3323668457$				$D_{19}$ (as 19T2)	trivial	$2$	$9$	$1152808.1284$
19.1.714...419.1	x^19 + 19x^15 - 19x^14 - 19x^13 + 171x^12 + 19x^11 - 266x^10 + 19x^9 + 475x^8 + 741x^7 + 437x^6 + 38x^5 - 38x^4 - 19x^3 + 1	$19$	[1,9]	$-\,19^{21}$	$1$	$25.9035473939$			not computed	$C_{19}:C_{6}$ (as 19T4)	trivial	$2$	$9$	$1437945.22979$
19.1.173...823.1	x^19 + 9x^17 - 10x^16 + 8x^15 - 45x^14 + 39x^13 + 7x^12 + 42x^11 - 36x^10 - 60x^9 + 9x^8 + 55x^7 + 63x^6 + 15x^5 - 88x^4 - 7x^3 + 27x^2 + 51x + 1	$19$	[1,9]	$-\,1063^{9}$	$1$	$27.140698466$				$D_{19}$ (as 19T2)	trivial	$2$	$9$	$2724154.30052$
19.1.512...799.1	x^19 - 3x^18 + 17x^17 - 47x^16 + 135x^15 - 310x^14 + 709x^13 - 1319x^12 + 2423x^11 - 3757x^10 + 5497x^9 - 6561x^8 + 7142x^7 - 5699x^6 + 4212x^5 - 1490x^4 + 482x^3 + 408x^2 - 210x + 49	$19$	[1,9]	$-\,11^{9}\cdot 109^{9}$	$2$	$28.7334671769$			not computed	$D_{19}$ (as 19T2)	trivial	$2$	$9$	$2481320.5796$
19.3.787...824.1	x^19 - 2x^18 + 7x^16 - 10x^15 - x^14 + 19x^13 - 19x^12 - 9x^11 + 33x^10 - 19x^9 - 20x^8 + 33x^7 - 9x^6 - 18x^5 + 17x^4 - 3x^3 - 5x^2 + 4x - 1	$19$	[3,8]	$2^{8}\cdot 317\cdot 25373\cdot 137363\cdot 27854432176313$	$5$	$29.3922902441$			not computed	$S_{19}$ (as 19T8)	trivial	$2$	$10$	$6223827.226$
19.1.206...091.1	x^19 + 2x - 1	$19$	[1,9]	$-\,7\cdot 233\cdot 12649189464522827348824661$	$3$	$30.9198742421$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$6403224.03446$
19.1.223...888.1	x^19 + 4x - 4	$19$	[1,9]	$-\,2^{18}\cdot 1699471\cdot 109607929\cdot 458633653$	$4$	$31.0537295863$			not computed	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$8836400.64766$
19.1.473...375.1	x^19 - 6x^18 + 18x^17 - 22x^16 - 38x^15 + 219x^14 - 403x^13 + 380x^12 - 536x^11 + 1378x^10 - 1608x^9 + 691x^8 - 1073x^7 + 1881x^6 - 757x^5 + 716x^4 - 1464x^3 + 513x^2 - 10x + 295	$19$	[1,9]	$-\,5^{9}\cdot 307^{9}$	$2$	$32.3004990658$				$D_{19}$ (as 19T2)	trivial	$2$	$9$	$26027741.7153$
19.1.495...343.1	x^19 - 9x^18 + 24x^17 - 6x^16 - 42x^15 + 4x^14 + 34x^13 + 74x^12 + 46x^11 - 238x^10 - 49x^9 + 181x^8 + 195x^7 + 116x^6 - 193x^5 - 275x^4 + 106x^3 - 8x^2 + 121x - 1	$19$	[1,9]	$-\,1543^{9}$	$1$	$32.3801306357$				$D_{19}$ (as 19T2)	trivial	$2$	$9$	$17317158.8896$
19.1.101...431.1	x^19 - 5x^18 + 11x^17 - 10x^16 + 3x^15 + 3x^14 - 80x^13 + 481x^12 - 1180x^11 + 1220x^10 + 888x^9 - 5070x^8 + 8854x^7 - 9440x^6 + 6893x^5 - 3748x^4 + 2592x^3 - 2790x^2 + 2673x - 1053	$19$	[1,9]	$-\,3^{9}\cdot 557^{9}$	$2$	$33.6258332676$				$D_{19}$ (as 19T2)	trivial	$2$	$9$	$191261859.157$
19.7.105...804.1	x^19 - 3x^18 - x^17 + 15x^16 - 22x^15 - 6x^14 + 59x^13 - 70x^12 - 6x^11 + 106x^10 - 107x^9 + 92x^7 - 73x^6 - x^5 + 35x^4 - 19x^3 - x^2 + 4x - 1	$19$	[7,6]	$2^{2}\cdot 131\cdot 149\cdot 397\cdot 20117\cdot 218819\cdot 773146117559$	$7$	$33.6928527152$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$12$	$52861133.6694$
19.1.197...516.1	x^19 - 3x^18 + 2x^17 + 4x^16 - 8x^15 + 14x^13 - 9x^12 - 16x^11 + 21x^10 + 8x^9 - 25x^8 + 2x^7 + 16x^6 - 4x^5 - 8x^4 + 2x^3 + 3x^2 - x - 1	$19$	[1,9]	$-\,2^{2}\cdot 49323595893763542101396994379$	$2$	$34.8215535648$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$20856736.7017$
19.1.231...871.1	x^19 - 6x^18 + 18x^17 - 39x^16 + 73x^15 - 200x^14 + 265x^13 + 305x^12 - 931x^11 + 1905x^10 - 5214x^9 + 10284x^8 - 13343x^7 + 12719x^6 - 8662x^5 + 4443x^4 - 1732x^3 + 614x^2 - 152x + 39	$19$	[1,9]	$-\,1831^{9}$	$1$	$35.1142949338$				$D_{19}$ (as 19T2)	trivial	$2$	$9$	$34462435.5384$
19.1.239...368.1	x^19 - 3x^18 + 2x^17 + 4x^16 - 8x^15 + 14x^13 - 9x^12 - 16x^11 + 21x^10 + 8x^9 - 25x^8 + 2x^7 + 17x^6 - 4x^5 - 9x^4 + 2x^3 + 3x^2 - x - 1	$19$	[1,9]	$-\,2^{7}\cdot 7\cdot 60259\cdot 4440286064038502416537$	$4$	$35.180511669$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$21087865.9745$
19.1.436...528.1	x^19 - 8x - 8	$19$	[1,9]	$-\,2^{18}\cdot 17\cdot 8627\cdot 11343650175290580793$	$4$	$36.306051933$			not computed	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$47279371.8637$
19.1.477...752.1	x^19 - 4x - 4	$19$	[1,9]	$-\,2^{18}\cdot 593\cdot 10949399\cdot 280461391706269$	$4$	$36.4791875178$			not computed	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$25714895.7196$
19.1.498...864.1	x^19 - 2x - 2	$19$	[1,9]	$-\,2^{18}\cdot 11\cdot 29\cdot 8255287577\cdot 721386928637$	$5$	$36.5605029997$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$44496889.6897$
19.1.518...552.1	x^19 - x - 2	$19$	[1,9]	$-\,2^{19}\cdot 821\cdot 883013\cdot 15385297\cdot 88689509$	$5$	$36.6386877755$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$42948347.6249$
19.1.518...855.1	x^19 - x - 4	$19$	[1,9]	$-\,5\cdot 103726168442653430174403870371$	$2$	$36.6386879218$			not computed	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$53039958.1922$
19.1.518...976.1	x^19 - 2	$19$	[1,9]	$-\,2^{18}\cdot 19^{19}$	$2$	$36.6386879218$			✓	$F_{19}$ (as 19T6)	trivial	$2$	$9$	$47980973.6594$
19.1.539...088.1	x^19 + 2x - 2	$19$	[1,9]	$-\,2^{18}\cdot 7\cdot 47\cdot 1031\cdot 108139\cdot 56081694178207$	$6$	$36.7139803836$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$30572994.7677$
19.1.601...424.1	x^19 + 8x - 8	$19$	[1,9]	$-\,2^{18}\cdot 46553428447\cdot 49259334849493$	$3$	$36.9245102701$			not computed	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$28122221.8245$
19.9.159...156.1	x^19 - 3x^18 - 8x^17 + 30x^16 + 16x^15 - 115x^14 + 31x^13 + 208x^12 - 175x^11 - 165x^10 + 280x^9 + 5x^8 - 206x^7 + 82x^6 + 75x^5 - 54x^4 - 13x^3 + 13x^2 + x - 1	$19$	[9,5]	$-\,2^{2}\cdot 937\cdot 971\cdot 4676220259\cdot 93910895860973$	$5$	$38.8744917393$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$13$	$222480440.47$
19.1.207...120.1	x^19 - 4x - 8	$19$	[1,9]	$-\,2^{20}\cdot 5\cdot 928238261\cdot 426273972622159$	$4$	$39.4118910595$			not computed	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$110775507.502$
19.1.386...375.1	x^19 + 19x^17 + 152x^15 + 665x^13 + 1729x^11 + 2717x^9 + 2508x^7 + 1254x^5 + 285x^3 + 19x - 1	$19$	[1,9]	$-\,5^{9}\cdot 19^{19}$	$2$	$40.7234586539$			✓	$F_{19}$ (as 19T6)	trivial	$2$	$9$	$123041861.807$
19.7.832...904.1	x^19 - 3x^18 - x^17 + 15x^16 - 22x^15 - 6x^14 + 59x^13 - 70x^12 - 6x^11 + 106x^10 - 107x^9 - x^8 + 92x^7 - 72x^6 - x^5 + 35x^4 - 19x^3 - x^2 + 4x - 1	$19$	[7,6]	$2^{10}\cdot 2746819\cdot 2958679616604904629509$	$3$	$42.4014216337$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$12$	$409832342.529$
19.5.896...328.1	x^19 - 2x^18 - 3x^17 + 9x^16 + x^15 - 16x^14 + 5x^13 + 17x^12 - 10x^11 - 12x^10 + 10x^9 + x^8 + 3x^6 - 9x^5 + 2x^4 + 6x^3 - 5x^2 - x + 1	$19$	[5,7]	$-\,2^{4}\cdot 3947\cdot 1431584761\cdot 99216821342546749$	$4$	$42.5690720688$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$11$	$363184844.905$
19.5.239...200.1	x^19 - x^18 - 6x^17 + 7x^16 + 13x^15 - 21x^14 - 16x^13 + 41x^12 + 10x^11 - 51x^10 + 5x^9 + 43x^8 - 19x^7 - 24x^6 + 18x^5 + 5x^4 - 11x^3 + 2x^2 + 3x - 1	$19$	[5,7]	$-\,2^{3}\cdot 5^{2}\cdot 430709\cdot 19005923\cdot 14610723851226353$	$5$	$44.824396879$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$11$	$840306267.085$
19.1.331...008.1	x^19 + 4x - 8	$19$	[1,9]	$-\,2^{24}\cdot 311\cdot 13913\cdot 49356007\cdot 9263974663$	$5$	$45.6039040723$			not computed	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$844213349.401$
19.3.457...029.1	x^19 - 3x - 1	$19$	[3,8]	$15451\cdot 1192721\cdot 1892107519\cdot 1311498030721$	$4$	$46.37957716$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$10$	$278595712.583$
19.1.457...987.1	x^19 + 3x - 1	$19$	[1,9]	$-\,577\cdot 70079\cdot 1130954781811714100492789$	$3$	$46.3795773712$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$356764768.985$
19.1.462...984.1	x^19 + 3x - 2	$19$	[1,9]	$-\,2^{19}\cdot 613\cdot 7331\cdot 3070062337\cdot 6393898213$	$5$	$46.407113236$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$1011018071.22$
19.1.629...707.1	x^19 - 9x - 9	$19$	[1,9]	$-\,3^{18}\cdot 125471\cdot 142573\cdot 90800058249161$	$4$	$53.2421064555$			not computed	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$682842465.233$
19.1.720...723.1	x^19 - 3x - 3	$19$	[1,9]	$-\,3^{18}\cdot 30011\cdot 461269\cdot 134390022739373$	$4$	$53.6237363277$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$1413210922.08$
19.1.766...619.1	x^19 - 2x - 3	$19$	[1,9]	$-\,3^{18}\cdot 109\cdot 2111\cdot 2503\cdot 3435034858449743$	$5$	$53.7975620938$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$1389263095.55$
19.1.766...307.1	x^19 - x - 3	$19$	[1,9]	$-\,3^{18}\cdot 733\cdot 5827\cdot 8053\cdot 2874523\cdot 20009947$	$6$	$53.7976382997$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$1320313121.52$
19.1.766...731.1	x^19 - 3	$19$	[1,9]	$-\,3^{18}\cdot 19^{19}$	$2$	$53.7976382998$			✓	$F_{19}$ (as 19T6)	trivial	$2$	$9$	$1832073247.14$
19.1.766...155.1	x^19 + x - 3	$19$	[1,9]	$-\,3^{18}\cdot 5\cdot 11\cdot 277\cdot 1202769413\cdot 107967633989$	$6$	$53.7976382999$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$1322096028.33$
19.13.801...664.1	x^19 - 2x^18 - 18x^17 + 32x^16 + 132x^15 - 202x^14 - 502x^13 + 645x^12 + 1045x^11 - 1122x^10 - 1176x^9 + 1078x^8 + 700x^7 - 557x^6 - 220x^5 + 151x^4 + 34x^3 - 20x^2 - 2x + 1	$19$	[13,3]	$-\,2^{3}\cdot 13^{2}\cdot 17\cdot 3229\cdot 34365587\cdot 85132367\cdot 3692009831$	$7$	$53.9247520599$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$15$	$23798894722.8$
19.1.812...739.1	x^19 + 3x - 3	$19$	[1,9]	$-\,3^{18}\cdot 581393\cdot 3605923841336588507$	$3$	$53.9619752737$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$1119576153.28$
19.1.903...755.1	x^19 + 9x - 9	$19$	[1,9]	$-\,3^{18}\cdot 5\cdot 7\cdot 11\cdot 17\cdot 293990087\cdot 1212233453773$	$7$	$54.2658868088$			not computed	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$1386849912.1$
19.9.138...476.1	x^19 - 2x^18 - 14x^17 + 23x^16 + 83x^15 - 104x^14 - 274x^13 + 234x^12 + 555x^11 - 274x^10 - 708x^9 + 162x^8 + 554x^7 - 50x^6 - 246x^5 + 17x^4 + 56x^3 - 7x^2 - 5x + 1	$19$	[9,5]	$-\,2^{2}\cdot 34\!\cdots\!19$	$2$	$55.505833971$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$13$	$8259829376.29$
19.1.171...279.1	x^19 + 7x - 4	$19$	[1,9]	$-\,17\!\cdots\!79$	$1$	$56.1208431643$			not computed	$S_{19}$ (as 19T8)	trivial	$2$	$9$	$3321587861.16$
19.13.610...484.1	x^19 - 3x^18 - 12x^17 + 40x^16 + 52x^15 - 216x^14 - 88x^13 + 614x^12 + 8x^11 - 987x^10 + 143x^9 + 904x^8 - 163x^7 - 461x^6 + 72x^5 + 128x^4 - 14x^3 - 18x^2 + x + 1	$19$	[13,3]	$-\,2^{2}\cdot 90313\cdot 16881409121807\cdot 1000636759045331$	$4$	$60.0045203941$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$15$	$61782008553.5$