Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (1-50 of 233741 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
3.1.451.1	$x^{3} - x^{2} - 5 x + 8$	$3$	[1,1]	$-\,11\cdot 41$	$2$	$7.66876649057$	$21.236760581595302$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$3.57573413339$
3.1.492.1	$x^{3} - x^{2} + 3 x + 3$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 41$	$3$	$7.89444677297$	$17.60512931716603$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$4.42072409068$
3.3.697.1	$x^{3} - 7 x - 5$	$3$	[3,0]	$17\cdot 41$	$2$	$8.86633751079$	$26.40075756488817$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$2.71184965988$
3.1.984.1	$x^{3} - x^{2} - 12$	$3$	[1,1]	$-\,2^{3}\cdot 3\cdot 41$	$3$	$9.94637966654$	$31.368774282716245$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$9.97919841126$
3.1.1107.1	$x^{3} + 6 x - 3$	$3$	[1,1]	$-\,3^{3}\cdot 41$	$2$	$10.3446517211$	$23.06924557594881$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$3.29174765018$
3.1.1599.1	$x^{3} + 3 x - 23$	$3$	[1,1]	$-\,3\cdot 13\cdot 41$	$3$	$11.6936337636$	$39.98749804626441$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$4.46392196445$
3.1.1763.1	$x^{3} + 11 x - 8$	$3$	[1,1]	$-\,41\cdot 43$	$2$	$12.0804775917$	$41.98809355043403$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$6.01867017906$
3.1.1927.1	$x^{3} - x^{2} + 2 x - 9$	$3$	[1,1]	$-\,41\cdot 47$	$2$	$12.4440163071$	$43.89760813529594$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$2.35003381942$
3.1.2091.1	$x^{3} - x^{2} - x - 26$	$3$	[1,1]	$-\,3\cdot 17\cdot 41$	$3$	$12.7874714651$	$45.727453460694704$				$S_3$ (as 3T2)	trivial	$2$	$1$	$10.5941817144$
3.1.2132.1	$x^{3} - x^{2} - 3 x + 19$	$3$	[1,1]	$-\,2^{2}\cdot 13\cdot 41$	$3$	$12.8705093209$	$46.17358552246078$				$S_3$ (as 3T2)	trivial	$2$	$1$	$10.7300504916$
3.3.2296.1	$x^{3} - x^{2} - 14 x - 14$	$3$	[3,0]	$2^{3}\cdot 7\cdot 41$	$3$	$13.1924045682$	$47.916594202843754$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$14.2655509459$
3.1.2747.1	$x^{3} - x^{2} + x + 30$	$3$	[1,1]	$-\,41\cdot 67$	$2$	$14.0051001826$	$52.41183072551463$				$S_3$ (as 3T2)	trivial	$2$	$1$	$17.1384895724$
3.1.2911.1	$x^{3} - x^{2} + 8 x - 9$	$3$	[1,1]	$-\,41\cdot 71$	$2$	$14.2784391528$	$53.95368384086484$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$2.22229249028$
3.3.2993.1	$x^{3} - x^{2} - 12 x + 17$	$3$	[3,0]	$41\cdot 73$	$2$	$14.4112694704$	$54.70831746635972$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$7.51407984191$
3.1.3075.1	$x^{3} - x^{2} - 3 x + 12$	$3$	[1,1]	$-\,3\cdot 5^{2}\cdot 41$	$3$	$14.541695288$	$32.42892547103848$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$15.1066430535$
3.1.3116.1	$x^{3} - x^{2} + x - 11$	$3$	[1,1]	$-\,2^{2}\cdot 19\cdot 41$	$3$	$14.6060399104$	$44.305270518711566$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$9.32643149743$
3.1.3444.1	$x^{3} - x^{2} - 12 x - 24$	$3$	[1,1]	$-\,2^{2}\cdot 3\cdot 7\cdot 41$	$4$	$15.1015334027$	$58.68560300448484$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$22.2657969372$
3.1.4428.1	$x^{3} + 6 x - 38$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 41$	$3$	$16.4211110244$	$36.620144695373874$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$3.65760853101$
3.1.4428.2	$x^{3} + 12 x - 20$	$3$	[1,1]	$-\,2^{2}\cdot 3^{3}\cdot 41$	$3$	$16.4211110244$	$36.620144695373874$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$4.14689670911$
3.1.4715.1	$x^{3} - 13 x - 32$	$3$	[1,1]	$-\,5\cdot 23\cdot 41$	$3$	$16.7684877919$	$68.66585760041157$				$S_3$ (as 3T2)	trivial	$2$	$1$	$13.1483780435$
3.1.4920.1	$x^{3} - x^{2} - 10 x + 22$	$3$	[1,1]	$-\,2^{3}\cdot 3\cdot 5\cdot 41$	$4$	$17.0080699863$	$70.14271166700073$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$30.5407656957$
3.1.5371.1	$x^{3} - x^{2} - 15 x - 22$	$3$	[1,1]	$-\,41\cdot 131$	$2$	$17.5126439237$	$73.287106642301$			✓	$S_3$ (as 3T2)	$[2]$	$2$	$1$	$7.37403019552$
3.1.5535.1	$x^{3} - 3 x - 43$	$3$	[1,1]	$-\,3^{3}\cdot 5\cdot 41$	$3$	$17.6891056199$	$51.58440129745782$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$6.85433781231$
3.1.5576.1	$x^{3} - x^{2} + x - 29$	$3$	[1,1]	$-\,2^{3}\cdot 17\cdot 41$	$3$	$17.7326750216$	$74.67261881037788$				$S_3$ (as 3T2)	trivial	$2$	$1$	$13.6693037397$
3.1.5699.1	$x^{3} - x^{2} + 11 x + 2$	$3$	[1,1]	$-\,41\cdot 139$	$2$	$17.8621151868$	$75.49172140042907$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$9.21811203901$
3.1.5740.1	$x^{3} - x^{2} - x + 15$	$3$	[1,1]	$-\,2^{2}\cdot 5\cdot 7\cdot 41$	$4$	$17.9048476826$	$60.13296444711741$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$17.7273422451$
3.1.6068.1	$x^{3} - x^{2} - 3 x - 29$	$3$	[1,1]	$-\,2^{2}\cdot 37\cdot 41$	$3$	$18.2395949946$	$77.89736837660179$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$20.1752552719$
3.1.6232.1	$x^{3} - x^{2} + 17 x - 21$	$3$	[1,1]	$-\,2^{3}\cdot 19\cdot 41$	$3$	$18.4024571388$	$78.9430174239622$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$25.8810435226$
3.3.6396.1	$x^{3} - x^{2} - 20 x + 24$	$3$	[3,0]	$2^{2}\cdot 3\cdot 13\cdot 41$	$4$	$18.5624865376$	$79.97499609252883$				$S_3$ (as 3T2)	trivial	$2$	$2$	$40.0307498197$
3.3.6601.1	$x^{3} - 13 x - 9$	$3$	[3,0]	$7\cdot 23\cdot 41$	$3$	$18.7587218682$	$81.24653838779841$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$20.2402177624$
3.1.6888.1	$x^{3} - x^{2} - 8 x + 36$	$3$	[1,1]	$-\,2^{3}\cdot 3\cdot 7\cdot 41$	$4$	$19.0267398198$	$82.99397568498571$				$S_3$ (as 3T2)	trivial	$2$	$1$	$36.710086358$
3.1.7052.1	$x^{3} - x^{2} + 7 x - 17$	$3$	[1,1]	$-\,2^{2}\cdot 41\cdot 43$	$3$	$19.1765628374$	$66.65194387209816$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$2.68537313887$
3.1.7052.2	$x^{3} - x^{2} + 3 x - 17$	$3$	[1,1]	$-\,2^{2}\cdot 41\cdot 43$	$3$	$19.1765628374$	$66.65194387209816$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$4.20757937446$
3.1.7052.3	$x^{3} - x^{2} + 11 x + 43$	$3$	[1,1]	$-\,2^{2}\cdot 41\cdot 43$	$3$	$19.1765628374$	$66.65194387209816$			✓	$S_3$ (as 3T2)	$[3]$	$2$	$1$	$8.5827972619$
3.1.7175.1	$x^{3} - x^{2} + 2 x + 32$	$3$	[1,1]	$-\,5^{2}\cdot 7\cdot 41$	$3$	$19.2874124836$	$49.53600189237178$				$S_3$ (as 3T2)	trivial	$2$	$1$	$38.1878377973$
3.1.7339.1	$x^{3} - x^{2} + 11 x + 6$	$3$	[1,1]	$-\,41\cdot 179$	$2$	$19.4332585701$	$85.66796367370944$			✓	$S_3$ (as 3T2)	$[5]$	$2$	$1$	$3.93374993166$
3.1.7831.1	$x^{3} + 19 x - 12$	$3$	[1,1]	$-\,41\cdot 191$	$2$	$19.8581631601$	$88.4929375713113$				$S_3$ (as 3T2)	$[7]$	$2$	$1$	$6.0476012547$
3.1.8036.1	$x^{3} + 14 x - 28$	$3$	[1,1]	$-\,2^{2}\cdot 7^{2}\cdot 41$	$3$	$20.0299551122$	$46.86197816804901$				$S_3$ (as 3T2)	$[3]$	$2$	$1$	$5.30367610236$
3.1.8200.1	$x^{3} - x^{2} + 2 x - 18$	$3$	[1,1]	$-\,2^{3}\cdot 5^{2}\cdot 41$	$3$	$20.1652967522$	$52.956213540525944$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$27.7623638038$
3.1.8323.1	$x^{3} - x^{2} + 7 x + 14$	$3$	[1,1]	$-\,7\cdot 29\cdot 41$	$3$	$20.2656232631$	$91.23047736365298$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$21.6302707516$
3.3.8692.1	$x^{3} - x^{2} - 13 x - 1$	$3$	[3,0]	$2^{2}\cdot 41\cdot 53$	$3$	$20.5607951365$	$73.99741132528298$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$16.9558131292$
3.1.8815.1	$x^{3} + 13 x - 1$	$3$	[1,1]	$-\,5\cdot 41\cdot 43$	$3$	$20.6573261063$	$93.888231424391$			✓	$S_3$ (as 3T2)	$[5]$	$2$	$1$	$2.56540400654$
3.1.8979.1	$x^{3} - x^{2} + 25 x - 36$	$3$	[1,1]	$-\,3\cdot 41\cdot 73$	$3$	$20.7846472012$	$94.75758544834287$				$S_3$ (as 3T2)	trivial	$2$	$1$	$28.4953200144$
3.1.9143.1	$x^{3} - x^{2} - 10 x - 19$	$3$	[1,1]	$-\,41\cdot 223$	$2$	$20.9104272503$	$95.61903576171431$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$7.45296754252$
3.1.9471.1	$x^{3} - x^{2} - 12 x - 21$	$3$	[1,1]	$-\,3\cdot 7\cdot 11\cdot 41$	$4$	$21.1575452739$	$97.31906288081488$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$13.6166546597$
3.1.9512.1	$x^{3} - x^{2} + 21 x - 17$	$3$	[1,1]	$-\,2^{3}\cdot 29\cdot 41$	$3$	$21.1880316925$	$97.52948272189288$			✓	$S_3$ (as 3T2)	trivial	$2$	$1$	$18.7585968591$
3.1.9676.1	$x^{3} - x^{2} + 11 x - 39$	$3$	[1,1]	$-\,2^{2}\cdot 41\cdot 59$	$3$	$21.3091087875$	$78.0736705899716$				$S_3$ (as 3T2)	trivial	$2$	$1$	$15.8255434722$
3.3.9676.1	$x^{3} - 22 x - 12$	$3$	[3,0]	$2^{2}\cdot 41\cdot 59$	$3$	$21.3091087875$	$98.3666610188635$				$S_3$ (as 3T2)	trivial	$2$	$2$	$61.8715966852$
3.1.9799.1	$x^{3} - x^{2} + 26 x + 19$	$3$	[1,1]	$-\,41\cdot 239$	$2$	$21.3990217039$	$98.98989847454133$				$S_3$ (as 3T2)	trivial	$2$	$1$	$13.6687063253$
3.3.10004.1	$x^{3} - 14 x - 6$	$3$	[3,0]	$2^{2}\cdot 41\cdot 61$	$3$	$21.547219097$	$79.385925021846$			✓	$S_3$ (as 3T2)	trivial	$2$	$2$	$26.7466525425$

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