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 332 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
9.1.404197705.1	$x^{9} + x - 1$	$9$	[1,4]	$5\cdot 197\cdot 410353$	$3$	$9.04249349085$	$20104.66873639056$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$4.58756375116$
9.1.3279991040.1	$x^{9} - 4 x - 4$	$9$	[1,4]	$2^{8}\cdot 5\cdot 223\cdot 11491$	$4$	$11.4108812065$	$6628.2451755394795$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$21.3163295323$
9.1.396450145280.1	$x^{9} - 4 x - 8$	$9$	[1,4]	$2^{10}\cdot 5\cdot 7\cdot 19\cdot 577\cdot 1009$	$6$	$19.4396132382$	$50406.32331578275$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$560.145114611$
9.1.1551188000745.1	$x^{9} - 9 x - 9$	$9$	[1,4]	$3^{10}\cdot 5\cdot 17\cdot 29\cdot 10657$	$5$	$22.6213370554$	$19037.976075639$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$343.898243269$
9.1.2541882605545.1	$x^{9} + x - 3$	$9$	[1,4]	$5\cdot 73\cdot 6964061933$	$3$	$23.8973976316$	$1594328.2615399503$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$544.550029407$
9.3.4298866865920.1	$x^{9} - 4 x - 2$	$9$	[3,3]	$-\,2^{8}\cdot 5\cdot 11\cdot 23\cdot 29\cdot 167\cdot 2741$	$7$	$25.3341302756$	$239960.2100445629$			✓	$S_9$ (as 9T34)	trivial	$2$	$5$	$1439.07630026$
9.3.4397659090615.1	$x^{9} - 4 x - 1$	$9$	[3,3]	$-\,5\cdot 7\cdot 31\cdot 67\cdot 101\cdot 307\cdot 1951$	$7$	$25.3981682299$	$2097059.6297232467$			✓	$S_9$ (as 9T34)	trivial	$2$	$5$	$1580.88554178$
9.1.5950778711040.1	$x^{9} - 18 x^{5} + 81 x - 128$	$9$	[1,4]	$2^{10}\cdot 3^{19}\cdot 5$	$3$	$26.2661904533$	$133.8680609318145$				$S_9$ (as 9T34)	trivial	$2$	$4$	$2399.94720702$
9.3.6604518850560.1	$x^{9} - 3 x^{8} + 8 x^{6} - 12 x^{5} + 12 x^{4} - 24 x^{2} + 30 x - 10$	$9$	[3,3]	$-\,2^{26}\cdot 3^{9}\cdot 5$	$3$	$26.5721562934$	$92.47043679495332$			?	$S_9$ (as 9T34)	trivial	$2$	$5$	$5209.25032274$
9.3.8916099916815.1	$x^{9} - 9 x - 1$	$9$	[3,3]	$-\,3^{14}\cdot 5\cdot 7\cdot 13\cdot 17\cdot 241$	$6$	$27.4731416393$	$14907.993278036776$			?	$S_9$ (as 9T34)	trivial	$2$	$5$	$2439.94428228$
9.1.18797206913280.1	$x^{9} + 6 x - 2$	$9$	[1,4]	$2^{8}\cdot 3^{7}\cdot 5\cdot 6714823$	$4$	$29.8469018891$	$28058.574494395623$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$3406.44368632$
9.3.23803114844160.1	$x^{9} - 18 x^{5} + 81 x - 32$	$9$	[3,3]	$-\,2^{12}\cdot 3^{19}\cdot 5$	$3$	$30.6402739228$	$101.30104003445153$				$S_9$ (as 9T34)	trivial	$2$	$5$	$16286.2499058$
9.3.25290809521920.1	$x^{9} - 9 x - 4$	$9$	[3,3]	$-\,2^{8}\cdot 3^{19}\cdot 5\cdot 17$	$4$	$30.8473656339$	$309.77267330153774$			?	$S_9$ (as 9T34)	trivial	$2$	$5$	$6111.66539426$
9.1.25390005944320.1	$x^{9} + x - 4$	$9$	[1,4]	$2^{16}\cdot 5\cdot 77484149$	$3$	$30.8607856485$	$87106.7148426094$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$6065.86863645$
9.1.48616417935360.1	$x^{9} + 6 x - 4$	$9$	[1,4]	$2^{14}\cdot 3^{9}\cdot 5\cdot 11\cdot 2741$	$5$	$33.170625558$	$4359.5975344962335$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$9838.86072428$
9.1.162679417207360.1	$x^{9} + x - 6$	$9$	[1,4]	$2^{6}\cdot 5\cdot 508373178773$	$3$	$37.9347264281$	$2888032.1763909888$				$S_9$ (as 9T34)	trivial	$2$	$4$	$26329.5203288$
9.1.171617548402665.1	$x^{9} + 6 x - 3$	$9$	[1,4]	$3^{9}\cdot 5\cdot 653\cdot 2670467$	$4$	$38.1608435232$	$311704.6233424517$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$9636.51768135$
9.3.252934582763520.1	$x^{9} - 2 x^{8} - 12 x^{7} + 50 x^{6} - 22 x^{5} - 84 x^{4} + 64 x^{3} + 100 x^{2} - 144 x + 48$	$9$	[3,3]	$-\,2^{16}\cdot 3^{8}\cdot 5\cdot 7^{6}$	$4$	$39.8413683532$	$249.8624414996464$				$S_9$ (as 9T34)	$[3]$	$2$	$5$	$36203.6541804$
9.1.507799783342080.1	$x^{9} + 576 x - 1024$	$9$	[1,4]	$2^{18}\cdot 3^{18}\cdot 5$	$3$	$43.049274282$	$182.1753992493284$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$23634.8882986$
9.1.507799783342080.2	$x^{9} + 36 x - 32$	$9$	[1,4]	$2^{18}\cdot 3^{18}\cdot 5$	$3$	$43.049274282$	$124.71179384669587$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$27868.5090456$
9.1.642684100792320.1	$x^{9} - 18 x^{5} + 81 x - 192$	$9$	[1,4]	$2^{12}\cdot 3^{22}\cdot 5$	$3$	$44.1909218993$	$264.9318058624458$				$S_9$ (as 9T34)	trivial	$2$	$4$	$67539.2741159$
9.1.646319605541120.1	$x^{9} - 4 x - 6$	$9$	[1,4]	$2^{8}\cdot 5\cdot 7\cdot 47\cdot 163\cdot 191\cdot 49297$	$7$	$44.21862755$	$2942292.8794195116$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$43533.8848363$
9.1.819793334626560.1	$x^{9} + 6 x - 6$	$9$	[1,4]	$2^{8}\cdot 3^{9}\cdot 5\cdot 7\cdot 4648417$	$5$	$45.4023429429$	$78845.48415320994$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$21825.4961824$
9.1.1667228227338240.1	$x^{9} + 6 x - 8$	$9$	[1,4]	$2^{22}\cdot 3^{9}\cdot 5\cdot 7\cdot 577$	$5$	$49.1284184909$	$3530.7150427615916$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$45350.3153634$
9.1.1871806375804545.1	$x^{9} + 6 x - 9$	$9$	[1,4]	$3^{7}\cdot 5\cdot 557\cdot 307317251$	$4$	$49.764297791$	$2419285.7506032414$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$47563.15425$
9.1.2229003975896585.1	$x^{9} - 4 x - 7$	$9$	[1,4]	$5\cdot 173\cdot 2309\cdot 19559\cdot 57059$	$5$	$50.7394376093$	$47212328.643020615$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$33145.6550071$
9.1.2233402039184905.1	$x^{9} + x - 7$	$9$	[1,4]	$5\cdot 73\cdot 55373\cdot 110503489$	$4$	$50.7505516819$	$47258883.1775033$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$20004.5180781$
9.3.4266435204370935.1	$x^{9} - 9 x - 7$	$9$	[3,3]	$-\,3^{19}\cdot 5\cdot 73\cdot 89\cdot 113$	$5$	$54.5348227633$	$30687.71596394032$			✓	$S_9$ (as 9T34)	trivial	$2$	$5$	$37714.9615076$
9.3.6497295360950295.1	$x^{9} - 9 x - 3$	$9$	[3,3]	$-\,3^{18}\cdot 5\cdot 11\cdot 73\cdot 4177$	$5$	$57.1439543244$	$40390.35092088931$			✓	$S_9$ (as 9T34)	trivial	$2$	$5$	$41996.9326591$
9.3.6499738047133440.1	$x^{9} - 9 x - 2$	$9$	[3,3]	$-\,2^{8}\cdot 3^{19}\cdot 5\cdot 17\cdot 257$	$5$	$57.1463409829$	$5099.682549701437$			✓	$S_9$ (as 9T34)	trivial	$2$	$5$	$115613.804116$
9.1.6499837243555840.1	$x^{9} + x - 8$	$9$	[1,4]	$2^{25}\cdot 5\cdot 73\cdot 530713$	$4$	$57.1464378872$	$195547.89877271076$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$92575.7606043$
9.1.16672783653155465.1	$x^{9} - 4 x - 9$	$9$	[1,4]	$5\cdot 11\cdot 6553\cdot 19387\cdot 2386133$	$5$	$63.45200446$	$129123133.68701778$			✓	$S_9$ (as 9T34)	$[2, 2]$	$2$	$4$	$83921.6725702$
9.1.16677181716443785.1	$x^{9} + x - 9$	$9$	[1,4]	$5\cdot 43133\cdot 77329106329$	$3$	$63.453863999$	$129140163.0649574$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$50377.3104996$
9.3.109267739753840640.1	$x^{9} - 3 x^{8} + 18 x^{7} - 70 x^{6} - 252 x^{5} - 420 x^{4} - 420 x^{3} - 180 x^{2} + 36 x + 36$	$9$	[3,3]	$-\,2^{20}\cdot 3^{11}\cdot 5\cdot 7^{6}$	$4$	$78.1926214426$	$1480.1678578818953$				$S_9$ (as 9T34)	trivial	$2$	$5$	$2351654.23132$
9.3.208229648656711680.1	$x^{9} - 729 x - 648$	$9$	[3,3]	$-\,2^{14}\cdot 3^{26}\cdot 5$	$3$	$84.0006230588$	$431.705906662084$				$S_9$ (as 9T34)	trivial	$2$	$5$	$3190346.84585$
9.1.462210647237591040.1	$x^{9} - 1944 x - 3456$	$9$	[1,4]	$2^{31}\cdot 3^{16}\cdot 5$	$3$	$91.7825234522$	$328.6117385253229$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$928560.026413$
9.1.1480744168225505280.1	$x^{9} - 36 x^{7} + 486 x^{5} - 2916 x^{3} + 6561 x - 6144$	$9$	[1,4]	$2^{20}\cdot 3^{24}\cdot 5$	$3$	$104.458124897$	$448.27201889632886$				$S_9$ (as 9T34)	trivial	$2$	$4$	$2020021.19338$
9.3.132...440.2	$x^{9} - 3 x^{8} - 60 x^{7} + 116 x^{6} + 906 x^{5} - 894 x^{4} - 5428 x^{3} + 2268 x^{2} + 24057 x + 34869$	$9$	[3,3]	$-\,2^{20}\cdot 3^{11}\cdot 5\cdot 7^{6}\cdot 11^{2}$	$5$	$133.225196659$	$5011.558383234675$				$S_9$ (as 9T34)	trivial	$2$	$5$	$19816019.8356$
9.1.368...760.1	$x^{9} - 36 x^{7} + 486 x^{5} - 2916 x^{3} + 6561 x - 77824$	$9$	[1,4]	$2^{15}\cdot 3^{14}\cdot 5\cdot 19^{6}$	$4$	$149.303851928$	$1630.0163039196548$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$15559909.7461$
9.1.473...960.1	$x^{9} + 6561 x - 17496$	$9$	[1,4]	$2^{25}\cdot 3^{24}\cdot 5$	$3$	$153.52570916$	$787.2787016215781$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$10327955.1049$
9.3.533...080.1	$x^{9} - 5184 x - 9216$	$9$	[3,3]	$-\,2^{22}\cdot 3^{26}\cdot 5$	$3$	$155.548105413$	$540.367867105879$				$S_9$ (as 9T34)	trivial	$2$	$5$	$23896069.427$
9.1.561...360.1	$x^{9} + 486 x - 1296$	$9$	[1,4]	$2^{30}\cdot 3^{21}\cdot 5$	$3$	$156.451445609$	$650.7312305323685$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$7578466.00751$
9.3.710...440.1	$x^{9} - 36 x^{7} - 168 x^{6} - 378 x^{5} - 504 x^{4} - 420 x^{3} - 216 x^{2} - 63 x + 393208$	$9$	[3,3]	$-\,2^{24}\cdot 3^{25}\cdot 5$	$3$	$160.600468399$	$608.9193448797736$			?	$S_9$ (as 9T34)	trivial	$2$	$5$	$18228246.8729$
9.1.414...920.1	$x^{9} - 12 x^{7} - 16 x^{6} + 288 x^{5} - 648 x^{3} - 7344 x^{2} + 29160 x - 17280$	$9$	[1,4]	$2^{18}\cdot 3^{12}\cdot 5\cdot 29^{6}$	$4$	$195.35161084$	$881.6776227595121$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$35177267.8758$
9.1.426...640.1	$x^{9} + 81 x - 72$	$9$	[1,4]	$2^{25}\cdot 3^{26}\cdot 5$	$3$	$195.978332281$	$901.638320092541$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$31542162.4888$
9.3.113...040.1	$x^{9} - 157464 x - 419904$	$9$	[3,3]	$-\,2^{28}\cdot 3^{25}\cdot 5$	$3$	$218.54351142$	$939.0820054738981$			?	$S_9$ (as 9T34)	trivial	$2$	$5$	$85830169.2205$
9.1.454...160.1	$x^{9} + 39366 x - 104976$	$9$	[1,4]	$2^{30}\cdot 3^{25}\cdot 5$	$3$	$254.937352483$	$1299.604867349741$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$79668519.9334$
9.1.909...320.1	$x^{9} - 2519424 x - 13436928$	$9$	[1,4]	$2^{31}\cdot 3^{25}\cdot 5$	$3$	$275.347570357$	$1417.229157254299$			?	$S_9$ (as 9T34)	trivial	$2$	$4$	$110246687.921$
9.3.136...480.1	$x^{9} - 54 x - 48$	$9$	[3,3]	$-\,2^{30}\cdot 3^{26}\cdot 5$	$3$	$288.036114692$	$1390.79544137727$			?	$S_9$ (as 9T34)	trivial	$2$	$5$	$229151985.259$
9.1.180...760.1	$x^{9} - 3 x^{8} - 111 x^{7} + 389 x^{6} + 4173 x^{5} - 9219 x^{4} - 87209 x^{3} + 50283 x^{2} + 2781882 x - 9576858$	$9$	[1,4]	$2^{15}\cdot 3^{16}\cdot 5\cdot 37^{6}$	$4$	$297.209969569$	$2439.110646456212$				$S_9$ (as 9T34)	trivial	$2$	$4$	$1045586955.51$

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