Number field search results

Results (42 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
37.1.104...381.1	x^37 - x - 1	$37$	[1,18]	$983\cdot 10\!\cdots\!07$	$2$	$36.9898710435$			✓	$S_{37}$ (as 37T11)	trivial	$2$	$18$	$94459733489984.19$
37.1.106...653.1	x^37 + x - 1	$37$	[1,18]	$19\cdot 11323755688122007063\cdot 49\!\cdots\!49$	$3$	$37.0100301069$			✓	$S_{37}$ (as 37T11)	trivial	$2$	$18$	$232694775426930.7$
37.1.146...709.1	x^37 + 2x - 1	$37$	[1,18]	$13\cdot 79\cdot 3203\cdot 230203\cdot 34944191\cdot 52002217\cdot 4124383231\cdot 25\!\cdots\!59$	$8$	$65.3537130156$			✓	$S_{37}$ (as 37T11)	trivial	$2$	$18$	$9551296549801247000$
37.1.696...128.1	x^37 - 4x - 4	$37$	[1,18]	$2^{36}\cdot 233\cdot 373\cdot 78191\cdot 71872279\cdot 16291354255739\cdot 1273067852382060949050712307$	$7$	$72.5458784279$			not computed	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.710...320.1	x^37 - 2x - 2	$37$	[1,18]	$2^{36}\cdot 5\cdot 7\cdot 151\cdot 9239\cdot 119446257446842253309\cdot 17\!\cdots\!07$	$7$	$72.5866483199$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.725...376.1	x^37 - x - 2	$37$	[1,18]	$2^{36}\cdot 255111423183900271\cdot 31886261543528230373\cdot 1297568460899930754527$	$4$	$72.6266101467$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.725...736.1	x^37 - x - 4	$37$	[1,18]	$2^{38}\cdot 40158589\cdot 859997730921167\cdot 76\!\cdots\!63$	$4$	$72.6266101467$			not computed	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.725...512.1	x^37 - 2	$37$	[1,18]	$2^{36}\cdot 37^{37}$	$2$	$72.6266101467$			✓	$F_{37}$ (as 37T9)	not computed	$2$	$18$	$$
37.1.739...704.1	x^37 + 2x - 2	$37$	[1,18]	$2^{36}\cdot 11\cdot 13\cdot 29\cdot 8111\cdot 32\!\cdots\!17$	$6$	$72.6657957379$			✓	$S_{37}$ (as 37T11)	trivial	$2$	$18$	$109736008063969670000$
37.1.754...896.1	x^37 + 4x - 4	$37$	[1,18]	$2^{36}\cdot 41\cdot 11851181\cdot 1770736411\cdot 12\!\cdots\!31$	$5$	$72.7042350707$			not computed	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.3.479...851.1	x^37 - 3x - 1	$37$	[3,17]	$-\,11\cdot 103\cdot 13781\cdot 868727\cdot 1508693\cdot 35096465749296997\cdot 66\!\cdots\!61$	$7$	$98.0305695216$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$19$	$$
37.1.479...885.1	x^37 + 3x - 1	$37$	[1,18]	$5\cdot 17\cdot 23\cdot 503\cdot 8237\cdot 17707\cdot 6366766785751\cdot 52\!\cdots\!61$	$8$	$98.0305695216$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.652...077.1	x^37 + 3x - 3	$37$	[1,18]	$3^{36}\cdot 211\cdot 6139531\cdot 8271665508919\cdot 6321124050660239\cdot 6421792279973985077$	$6$	$98.8542412001$			not computed	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.153...189.1	x^37 - 3x - 3	$37$	[1,18]	$3^{36}\cdot 9598397\cdot 10\!\cdots\!97$	$3$	$107.663232105$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.158...365.1	x^37 - 2x - 3	$37$	[1,18]	$3^{36}\cdot 5\cdot 7\cdot 1493\cdot 137771\cdot 867792304013\cdot 16\!\cdots\!81$	$7$	$107.75261276$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.158...421.1	x^37 - x - 3	$37$	[1,18]	$3^{36}\cdot 10\!\cdots\!01$	$2$	$107.752612787$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.158...557.1	x^37 - 3	$37$	[1,18]	$3^{36}\cdot 37^{37}$	$2$	$107.752612787$			✓	$F_{37}$ (as 37T9)	not computed	$2$	$18$	$$
37.1.158...693.1	x^37 + x - 3	$37$	[1,18]	$3^{36}\cdot 19\cdot 349\cdot 4501649\cdot 1182640248703\cdot 29\!\cdots\!69$	$6$	$107.752612787$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.37.171...601.1	x^37 - x^36 - 72x^35 + 67x^34 + 2278x^33 - 1964x^32 - 41849x^31 + 33262x^30 + 497142x^29 - 362207x^28 - 4027127x^27 + 2672215x^26 + 22871279x^25 - 13719683x^24 - 92273266x^23 + 49606380x^22 + 265291071x^21 - 126402144x^20 - 540999671x^19 + 224635365x^18 + 773506030x^17 - 271832880x^16 - 761221384x^15 + 214848879x^14 + 502240682x^13 - 103923082x^12 - 213804070x^11 + 27920639x^10 + 55105551x^9 - 3603129x^8 - 7708785x^7 + 235974x^6 + 497852x^5 - 22640x^4 - 12819x^3 + 1020x^2 + 28x - 1	$37$	[37,0]	$149^{36}$	$1$	$130.15219727$		✓		$C_{37}$ (as 37T1)	trivial	$2$	$36$	$2217351755002491400000000000$
37.3.200...112.1	x^37 - 4x - 2	$37$	[3,17]	$-\,2^{36}\cdot 1181\cdot 156768103\cdot 3595021207\cdot 43\!\cdots\!67$	$5$	$130.707426027$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$19$	$$
37.3.200...107.1	x^37 - 4x - 1	$37$	[3,17]	$-\,53\cdot 139\cdot 27\!\cdots\!21$	$3$	$130.707426029$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$19$	$$
37.1.200...136.1	x^37 + 4x - 2	$37$	[1,18]	$2^{36}\cdot 249494962454898495919\cdot 11\!\cdots\!79$	$3$	$130.70742603$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.201...181.1	x^37 + 4x - 3	$37$	[1,18]	$3^{36}\cdot 839348831\cdot 15\!\cdots\!31$	$3$	$130.710209914$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.124...160.1	x^37 - 2x - 4	$37$	[1,18]	$2^{70}\cdot 5\cdot 7\cdot 47\cdot 64\!\cdots\!17$	$5$	$137.314984457$			not computed	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.124...256.1	x^37 + 2x - 4	$37$	[1,18]	$2^{70}\cdot 13\cdot 137\cdot 195791\cdot 10489284688357\cdot 5723750340436657\cdot 504174169295944373011$	$7$	$137.314984457$			not computed	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.498...464.1	x^37 - 3x - 4	$37$	[1,18]	$2^{73}\cdot 9739\cdot 174331\cdot 36662321\cdot 289516438999\cdot 95795519149931\cdot 3057074418307037$	$7$	$142.557415254$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.498...968.1	x^37 + x - 4	$37$	[1,18]	$2^{73}\cdot 19\cdot 311\cdot 20831443951883\cdot 42\!\cdots\!57$	$5$	$142.557418957$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.860...173.1	x^37 + 5x - 3	$37$	[1,18]	$3^{34}\cdot 7\cdot 17\cdot 439\cdot 4064647\cdot 22665391718591\cdot 10\!\cdots\!81$	$7$	$153.964267333$				$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.193...128.1	x^37 + 5x - 2	$37$	[1,18]	$2^{34}\cdot 7\cdot 8599\cdot 1088665069\cdot 284461581404201\cdot 60\!\cdots\!01$	$6$	$157.375956868$				$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.3.774...443.1	x^37 - 5x - 3	$37$	[3,17]	$-\,3^{36}\cdot 43\cdot 1907\cdot 62\!\cdots\!83$	$4$	$163.384281632$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$19$	$$
37.1.774...517.1	x^37 + 5x - 1	$37$	[1,18]	$7\cdot 47\cdot 23\!\cdots\!73$	$3$	$163.384282536$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.779...832.1	x^37 + 5x - 4	$37$	[1,18]	$2^{73}\cdot 7\cdot 37573\cdot 161999\cdot 10047643\cdot 4972224617011\cdot 387504669093621087013178459593$	$7$	$163.412628743$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.145...125.1	x^37 - 5x - 5	$37$	[1,18]	$5^{36}\cdot 563\cdot 175944697081\cdot 746724389353\cdot 13\!\cdots\!43$	$5$	$176.877946858$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.153...501.1	x^37 - 4x - 5	$37$	[1,18]	$15\!\cdots\!01$	$1$	$177.125257097$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.153...757.1	x^37 - 3x - 5	$37$	[1,18]	$47\cdot 4458653\cdot 39030547\cdot 4191145897\cdot 2748399402101\cdot 46040166590110289\cdot 35410190689086361595487217777$	$7$	$177.125319729$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.153...933.1	x^37 - 2x - 5	$37$	[1,18]	$7\cdot 34591\cdot 96167\cdot 163386011\cdot 40\!\cdots\!57$	$5$	$177.12531973$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.153...989.1	x^37 - x - 5	$37$	[1,18]	$11\cdot 107\cdot 359\cdot 60013\cdot 22231407377\cdot 27\!\cdots\!23$	$6$	$177.12531973$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.1.153...125.1	x^37 - 5	$37$	[1,18]	$5^{36}\cdot 37^{37}$	$2$	$177.12531973$			✓	$F_{37}$ (as 37T9)	not computed	$2$	$18$	$$
37.1.161...125.1	x^37 + 5x - 5	$37$	[1,18]	$5^{36}\cdot 7\cdot 17\cdot 39619\cdot 50081864423\cdot 2601293855703705209\cdot 18050801224775844479711$	$7$	$177.360848235$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$	$$
37.37.345...561.1	x^37 - x^36 - 108x^35 + 245x^34 + 4913x^33 - 17429x^32 - 115073x^31 + 605121x^30 + 1258904x^29 - 11895493x^28 + 1401577x^27 + 136786740x^26 - 218698801x^25 - 851925353x^24 + 2810760540x^23 + 1559768964x^22 - 17408647490x^21 + 14765496491x^20 + 52555917850x^19 - 112901823056x^18 - 30825357400x^17 + 320568348295x^16 - 255996383256x^15 - 343575615312x^14 + 697695088122x^13 - 135330997139x^12 - 635742178755x^11 + 559084397332x^10 + 98854779029x^9 - 379266961937x^8 + 152281955055x^7 + 65816775545x^6 - 70480276872x^5 + 12914339542x^4 + 6483753572x^3 - 3469705332x^2 + 579396241x - 30247313	$37$	[37,0]	$223^{36}$	$1$	$192.680233546$		✓		$C_{37}$ (as 37T1)	trivial	$2$	$36$	$2669696754256726600000000000000$
37.37.676...801.1	x^37 - x^36 - 288x^35 + 203x^34 + 35910x^33 - 17336x^32 - 2554843x^31 + 842615x^30 + 115283443x^29 - 27504461x^28 - 3475263507x^27 + 687931612x^26 + 71915662407x^25 - 13974595438x^24 - 1034496050617x^23 + 221330910643x^22 + 10365088714029x^21 - 2534502436630x^20 - 71813314605418x^19 + 19740632343658x^18 + 338381715805464x^17 - 99305962871851x^16 - 1055972317034939x^15 + 302779333586209x^14 + 2104618406390649x^13 - 505910437546894x^12 - 2560928454934750x^11 + 376597618487442x^10 + 1787314591059035x^9 - 20429122626927x^8 - 643936928000107x^7 - 89391122404607x^6 + 89662863870162x^5 + 25891375086732x^4 + 1113091773432x^3 - 112807611860x^2 - 8478121776x - 123515969	$37$	[37,0]	$593^{36}$	$1$	$499.007725404$		✓		$C_{37}$ (as 37T1)	not computed	$2$	$36$	$$
37.37.813...681.1	x^37 - 666x^35 - 481x^34 + 193399x^33 + 256521x^32 - 32436827x^31 - 60004084x^30 + 3503452596x^29 + 8113398850x^28 - 257000630926x^27 - 704292185114x^26 + 13150853376643x^25 + 41268101524916x^24 - 474337598223255x^23 - 1672482254287228x^22 + 12032466243732809x^21 + 47286637172470867x^20 - 211502629431882231x^19 - 929675982328753625x^18 + 2498958523266151636x^17 + 12536142236443615902x^16 - 18791897342800992970x^15 - 113239929214497210129x^14 + 80927529107744817385x^13 + 663966210336111429023x^12 - 146546651897009713442x^11 - 2439258160361411529393x^10 - 154326326264692800324x^9 + 5386184266991634344483x^8 + 1055793633392402952768x^7 - 6769150214799915444440x^6 - 1552196159553019851407x^5 + 4355671676506075568364x^4 + 921754431147330625307x^3 - 1108584774969076393499x^2 - 217498966742521653325x + 51140551819476687829	$37$	[37,0]	$37^{72}$	$1$	$1126.25255021$		✓		$C_{37}$ (as 37T1)	not computed	$2$	$36$	$$