Number field search results

Results (49 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
31.1.168...431.1	x^31 - x - 1	$31$	[1,15]	$-\,4211\cdot 107951341831\cdot 1040542609867\cdot 35650774802780191673$	$4$	$30.9878668755$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$42212973871.16097$
31.1.172...431.1	x^31 + x - 1	$31$	[1,15]	$-\,107\cdot 349\cdot 46\!\cdots\!17$	$3$	$31.0119923122$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$60402933903.83712$
31.1.365...111.1	x^31 + 2x - 1	$31$	[1,15]	$-\,71\cdot 6073\cdot 84\!\cdots\!17$	$3$	$46.0591112201$			not computed	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$38986878555233.18$
31.1.174...144.1	x^31 - 4x - 4	$31$	[1,15]	$-\,2^{30}\cdot 29161973\cdot 14898732471895043\cdot 37391233052164359356929$	$4$	$60.5324503205$			not computed	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$2698409433385651.0$
31.1.178...144.1	x^31 - 2x - 2	$31$	[1,15]	$-\,2^{30}\cdot 937\cdot 17\!\cdots\!63$	$3$	$60.5813478258$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$3069030481487575.5$
31.1.183...144.1	x^31 - x - 2	$31$	[1,15]	$-\,2^{31}\cdot 1433\cdot 3653617274537267\cdot 1630096334391835835360875373$	$4$	$60.6290892528$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$6213208850652677.0$
31.1.183...519.1	x^31 - x - 4	$31$	[1,15]	$-\,23\cdot 1693\cdot 3697\cdot 19843\cdot 14132537\cdot 75771043\cdot 5991663366536301415229073661$	$7$	$60.6290892528$			not computed	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$4169052629874545.0$
31.1.183...144.1	x^31 - 2	$31$	[1,15]	$-\,2^{30}\cdot 31^{31}$	$2$	$60.6290892528$			✓	$F_{31}$ (as 31T8)	trivial	$2$	$15$	$5190129910021260.0$
31.1.187...144.1	x^31 + 2x - 2	$31$	[1,15]	$-\,2^{30}\cdot 11\cdot 1489\cdot 1499\cdot 23334601\cdot 28850169461\cdot 1057614572100224186051$	$7$	$60.6757288558$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$5116384966428125.0$
31.1.192...144.1	x^31 + 4x - 4	$31$	[1,15]	$-\,2^{30}\cdot 7\cdot 90373\cdot 161611\cdot 54687761\cdot 3200213985295117341572815151$	$6$	$60.7213171385$			not computed	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$3952566540405579.5$
31.3.127...569.1	x^31 - 3x - 1	$31$	[3,14]	$7\cdot 17\cdot 23\cdot 15726392777460683\cdot 29\!\cdots\!39$	$5$	$80.6479693545$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$16$	$227786011641746100$
31.1.127...431.1	x^31 + 3x - 1	$31$	[1,15]	$-\,43\cdot 39047\cdot 455317\cdot 317197259\cdot 45044106017368643\cdot 11642845821394330173359$	$6$	$80.6479693545$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$253630612977039870$
31.1.127...144.1	x^31 + 3x - 2	$31$	[1,15]	$-\,2^{31}\cdot 59\cdot 316799009\cdot 31\!\cdots\!63$	$4$	$80.6483442561$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$1049301058301323900$
31.1.338...719.1	x^31 - 3x - 3	$31$	[1,15]	$-\,3^{30}\cdot 7\cdot 2713\cdot 14387\cdot 3413878991\cdot 72413150415649\cdot 243568924508677$	$7$	$89.655221097$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$1235026277671475000$
31.1.351...719.1	x^31 - 2x - 3	$31$	[1,15]	$-\,3^{30}\cdot 1069\cdot 745011551\cdot 21\!\cdots\!49$	$4$	$89.7618797049$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$2083870736834916600$
31.1.351...719.1	x^31 - x - 3	$31$	[1,15]	$-\,3^{31}\cdot 571\cdot 99\!\cdots\!87$	$3$	$89.7618800692$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$1630733111771600400$
31.1.351...719.1	x^31 - 3	$31$	[1,15]	$-\,3^{30}\cdot 31^{31}$	$2$	$89.7618800692$			✓	$F_{31}$ (as 31T8)	trivial	$2$	$15$	$2584759353644243000$
31.1.351...719.1	x^31 + x - 3	$31$	[1,15]	$-\,3^{30}\cdot 19\cdot 3539\cdot 25\!\cdots\!91$	$4$	$89.7618800692$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$1038806063023256300$
31.1.364...719.1	x^31 + 3x - 3	$31$	[1,15]	$-\,3^{30}\cdot 678106210770691935341\cdot 26082709826393492021802491$	$3$	$89.8648674064$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$980243888323008500$
31.1.194...831.1	x^31 + 4x - 3	$31$	[1,15]	$-\,3^{30}\cdot 59\cdot 10709\cdot 14\!\cdots\!49$	$4$	$94.8552726221$			not computed	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$4933387750736738000$
31.3.949...856.1	x^31 - 4x - 2	$31$	[3,14]	$2^{30}\cdot 2383\cdot 37\!\cdots\!43$	$3$	$107.530625739$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$16$	$36948458623552070000$
31.3.949...569.1	x^31 - 4x - 1	$31$	[3,14]	$24365060088671\cdot 38\!\cdots\!39$	$2$	$107.530625806$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$16$	$38197936820101820000$
31.1.949...431.1	x^31 + 4x - 1	$31$	[1,15]	$-\,7\cdot 13\!\cdots\!33$	$2$	$107.530625806$			✓	$S_{31}$ (as 31T12)	$[2]$	$2$	$15$	$20750959184225810000$
31.1.949...144.1	x^31 + 4x - 2	$31$	[1,15]	$-\,2^{30}\cdot 7\cdot 195469\cdot 212031575390627\cdot 30\!\cdots\!91$	$5$	$107.530625873$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$26578047987565236000$
31.1.491...664.1	x^31 - 2x - 4	$31$	[1,15]	$-\,2^{58}\cdot 18637\cdot 91\!\cdots\!13$	$3$	$113.391135691$			not computed	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$210828920582287920000$
31.1.491...664.1	x^31 + 2x - 4	$31$	[1,15]	$-\,2^{58}\cdot 11\cdot 15\!\cdots\!71$	$3$	$113.391135691$			not computed	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$94153833123094710000$
31.1.196...656.1	x^31 - 3x - 4	$31$	[1,15]	$-\,2^{30}\cdot 7\cdot 81987621103882733\cdot 1994715371164304797\cdot 16009667507940703067$	$5$	$118.576957979$			✓	$S_{31}$ (as 31T12)	not computed	$2$	$15$	$$
31.1.196...656.1	x^31 + x - 4	$31$	[1,15]	$-\,2^{30}\cdot 103\cdot 1946342156463328037\cdot 91\!\cdots\!79$	$4$	$118.576982698$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$367578496614054170000$
31.1.106...191.1	x^31 + 5x - 3	$31$	[1,15]	$-\,3^{30}\cdot 43\cdot 16293623473\cdot 73\!\cdots\!81$	$4$	$125.216113893$			not computed	$S_{31}$ (as 31T12)	not computed	$2$	$15$	$$
31.1.239...536.1	x^31 + 5x - 2	$31$	[1,15]	$-\,2^{30}\cdot 13\cdot 17\cdot 27768997\cdot 113656553679773909591\cdot 320037570123859568648600917$	$6$	$128.534850359$			not computed	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$1487371382989533200000$
31.3.958...281.1	x^31 - 5x - 3	$31$	[3,14]	$3^{30}\cdot 13\cdot 16690100963\cdot 21\!\cdots\!51$	$4$	$134.413266364$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$16$	$1258080429033531000000$
31.3.958...856.1	x^31 - 5x - 2	$31$	[3,14]	$2^{31}\cdot 15619263033943\cdot 55942004669294094613\cdot 510951109592180719533133$	$4$	$134.413282257$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$16$	$4907974822306732000000$
31.3.958...569.1	x^31 - 5x - 1	$31$	[3,14]	$13\cdot 1877\cdot 25841\cdot 202437701896105219\cdot 75\!\cdots\!11$	$5$	$134.413282257$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$16$	$1341618162426672300000$
31.1.958...431.1	x^31 + 5x - 1	$31$	[1,15]	$-\,59\cdot 18439\cdot 88\!\cdots\!31$	$3$	$134.413282257$			✓	$S_{31}$ (as 31T12)	not computed	$2$	$15$	$$
31.1.978...656.1	x^31 + 5x - 4	$31$	[1,15]	$-\,2^{30}\cdot 105767\cdot 86\!\cdots\!07$	$3$	$134.501409014$			✓	$S_{31}$ (as 31T12)	not computed	$2$	$15$	$$
31.1.149...375.1	x^31 - 5x - 5	$31$	[1,15]	$-\,5^{30}\cdot 443\cdot 26931473971\cdot 13\!\cdots\!27$	$4$	$146.863137605$			✓	$S_{31}$ (as 31T12)	not computed	$2$	$15$	$$
31.1.158...375.1	x^31 - 4x - 5	$31$	[1,15]	$-\,5^{30}\cdot 139\cdot 162071227763491\cdot 757645147032594015522973305823$	$4$	$147.157852638$			✓	$S_{31}$ (as 31T12)	not computed	$2$	$15$	$$
31.1.158...375.1	x^31 - 3x - 5	$31$	[1,15]	$-\,5^{30}\cdot 7\cdot 43132069\cdot 56\!\cdots\!73$	$4$	$147.158136144$			✓	$S_{31}$ (as 31T12)	not computed	$2$	$15$	$$
31.1.158...375.1	x^31 - 2x - 5	$31$	[1,15]	$-\,5^{30}\cdot 17\!\cdots\!83$	$2$	$147.158136182$			✓	$S_{31}$ (as 31T12)	not computed	$2$	$15$	$$
31.1.158...375.1	x^31 - x - 5	$31$	[1,15]	$-\,5^{31}\cdot 34\!\cdots\!31$	$2$	$147.158136182$			✓	$S_{31}$ (as 31T12)	not computed	$2$	$15$	$$
31.1.158...375.1	x^31 - 5	$31$	[1,15]	$-\,5^{30}\cdot 31^{31}$	$2$	$147.158136182$			✓	$F_{31}$ (as 31T8)	not computed	$2$	$15$	$$
31.1.158...375.1	x^31 + x - 5	$31$	[1,15]	$-\,5^{30}\cdot 19\cdot 173\cdot 2149711\cdot 24\!\cdots\!51$	$5$	$147.158136182$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$4634927539611405600000$
31.1.158...375.1	x^31 + 2x - 5	$31$	[1,15]	$-\,5^{30}\cdot 11\cdot 71\cdot 311\cdot 1667\cdot 209394034439\cdot 201326610321383981030559113$	$7$	$147.158136182$			✓	$S_{31}$ (as 31T12)	trivial	$2$	$15$	$4536078693224075000000$
31.1.158...375.1	x^31 + 3x - 5	$31$	[1,15]	$-\,5^{30}\cdot 190717\cdot 89\!\cdots\!59$	$3$	$147.15813622$			✓	$S_{31}$ (as 31T12)	not computed	$2$	$15$	$$
31.1.168...375.1	x^31 + 5x - 5	$31$	[1,15]	$-\,5^{30}\cdot 13\cdot 23\cdot 863\cdot 91923297263327\cdot 763023859796690773329733469$	$6$	$147.436395264$			✓	$S_{31}$ (as 31T12)	not computed	$2$	$15$	$$
31.31.606...801.1	x^31 - x^30 - 150x^29 + 117x^28 + 9434x^27 - 4958x^26 - 328880x^25 + 78328x^24 + 7098810x^23 + 507925x^22 - 100297691x^21 - 39217806x^20 + 950942678x^19 + 677567200x^18 - 6056859921x^17 - 6293114670x^16 + 25303767350x^15 + 35315191500x^14 - 65145555320x^13 - 122001770825x^12 + 87706314807x^11 + 253609179978x^10 - 19776440614x^9 - 299693882286x^8 - 98200795275x^7 + 175359843704x^6 + 113820457794x^5 - 30260338943x^4 - 38729335872x^3 - 5811762482x^2 + 1056847214x - 26458109	$31$	[31,0]	$311^{30}$	$1$	$258.433472772$		✓		$C_{31}$ (as 31T1)	not computed	$2$	$30$	$$
31.31.141...449.1	x^31 - x^30 - 180x^29 + 381x^28 + 13354x^27 - 40454x^26 - 531040x^25 + 2069355x^24 + 12295300x^23 - 60883682x^22 - 164683595x^21 + 1114070344x^20 + 1058778882x^19 - 13103530537x^18 + 1853849258x^17 + 99224120479x^16 - 91885359548x^15 - 467511308511x^14 + 762650059488x^13 + 1229830733203x^12 - 3225889300699x^11 - 1095874556276x^10 + 7495923118841x^9 - 2504773526476x^8 - 8920808783994x^7 + 7437366186489x^6 + 3836259163454x^5 - 6642200925120x^4 + 1200673450587x^3 + 1711910811444x^2 - 967097412303x + 151576217389	$31$	[31,0]	$373^{30}$	$1$	$308.141705804$		✓		$C_{31}$ (as 31T1)	trivial	$2$	$30$	$65100477933366770000000000000$
31.31.107...849.1	x^31 - x^30 - 330x^29 + 852x^28 + 43784x^27 - 173944x^26 - 2923572x^25 + 15562316x^24 + 100635650x^23 - 707709554x^22 - 1616621784x^21 + 17266725972x^20 + 7046247776x^19 - 243865756432x^18 + 142454592564x^17 + 2084163747748x^16 - 2521472241195x^15 - 10836712986085x^14 + 18499228115810x^13 + 32698257976552x^12 - 74538290301632x^11 - 47884603550112x^10 + 168256221920320x^9 + 4878741111552x^8 - 195294436805376x^7 + 62882730299136x^6 + 92885896276480x^5 - 43440624908288x^4 - 15171034030080x^3 + 6823763935232x^2 + 786648006656x + 5192548352	$31$	[31,0]	$683^{30}$	$1$	$553.334536638$		✓		$C_{31}$ (as 31T1)	trivial	$2$	$30$	$588096262939769340000000000000000000000000$
31.31.303...801.1	x^31 - 465x^29 - 341x^28 + 91078x^27 + 119908x^26 - 9914451x^25 - 18008892x^24 + 666449563x^23 + 1538774528x^22 - 28934386579x^21 - 83032233092x^20 + 817351924162x^19 + 2943382779538x^18 - 14471455469735x^17 - 68751097280499x^16 + 137645143880654x^15 + 1028543867187214x^14 - 144266178422457x^13 - 9110738641752719x^12 - 11199776062831713x^11 + 37846129267859005x^10 + 105950708850677777x^9 + 9682358886535270x^8 - 290542929220278846x^7 - 437492517497239584x^6 - 201727405103545942x^5 + 73256081844015542x^4 + 87563225965427030x^3 + 7669633084320922x^2 - 7522164033404415x - 310695313260929	$31$	[31,0]	$31^{60}$	$1$	$770.027976566$		✓		$C_{31}$ (as 31T1)	not computed	$2$	$30$	$$