Number field search results

Results (35 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
37.1.104...381.1	$x^{37} - x - 1$	$37$	[1,18]	$983\cdot 10\!\cdots\!07$	$2$	$36.9898710435$	$1.0221911561373473e+29$			✓	$S_{37}$ (as 37T11)	trivial	$2$	$18$	$94459733489984.19$
37.1.106...653.1	$x^{37} + x - 1$	$37$	[1,18]	$19\cdot 11323755688122007063\cdot 49\!\cdots\!49$	$3$	$37.0100301069$	$1.0325464790846705e+29$			✓	$S_{37}$ (as 37T11)	trivial	$2$	$18$	$232694775426930.7$
37.1.146...709.1	$x^{37} + 2 x - 1$	$37$	[1,18]	$13\cdot 79\cdot 3203\cdot 230203\cdot 34944191\cdot 52002217\cdot 4124383231\cdot 25\!\cdots\!59$	$8$	$65.3537130156$	$3.823841953282166e+33$			✓	$S_{37}$ (as 37T11)	trivial	$2$	$18$	$9551296549801247000$
37.1.696...128.1	$x^{37} - 4 x - 4$	$37$	[1,18]	$2^{36}\cdot 233\cdot 373\cdot 78191\cdot 71872279\cdot 16291354255739\cdot 1273067852382060949050712307$	$7$	$72.5458784279$	$1.975558468319023e+29$			?	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.710...320.1	$x^{37} - 2 x - 2$	$37$	[1,18]	$2^{36}\cdot 5\cdot 7\cdot 151\cdot 9239\cdot 119446257446842253309\cdot 17\!\cdots\!07$	$7$	$72.5866483199$	$1.9961992138047286e+29$			✓	$S_{37}$ (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]	$2^{38}\cdot 40158589\cdot 859997730921167\cdot 76\!\cdots\!63$	$4$	$72.6266101467$				?	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.739...704.1	$x^{37} + 2 x - 2$	$37$	[1,18]	$2^{36}\cdot 11\cdot 13\cdot 29\cdot 8111\cdot 32\!\cdots\!17$	$6$	$72.6657957379$	$2.0368533035272427e+29$			✓	$S_{37}$ (as 37T11)	trivial	$2$	$18$	$109736008063969670000$
37.1.754...896.1	$x^{37} + 4 x - 4$	$37$	[1,18]	$2^{36}\cdot 41\cdot 11851181\cdot 1770736411\cdot 12\!\cdots\!31$	$5$	$72.7042350707$	$2.056879048349089e+29$			?	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.3.479...851.1	$x^{37} - 3 x - 1$	$37$	[3,17]	$-\,11\cdot 103\cdot 13781\cdot 868727\cdot 1508693\cdot 35096465749296997\cdot 66\!\cdots\!61$	$7$	$98.0305695216$	$6.921308800624237e+36$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$19$
37.1.479...885.1	$x^{37} + 3 x - 1$	$37$	[1,18]	$5\cdot 17\cdot 23\cdot 503\cdot 8237\cdot 17707\cdot 6366766785751\cdot 52\!\cdots\!61$	$8$	$98.0305695216$	$6.921308800624239e+36$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.652...077.1	$x^{37} + 3 x - 3$	$37$	[1,18]	$3^{36}\cdot 211\cdot 6139531\cdot 8271665508919\cdot 6321124050660239\cdot 6421792279973985077$	$6$	$98.8542412001$	$6.073746714558556e+28$			?	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.153...189.1	$x^{37} - 3 x - 3$	$37$	[1,18]	$3^{36}\cdot 9598397\cdot 10\!\cdots\!97$	$3$	$107.663232105$	$2.946392829551214e+29$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.158...365.1	$x^{37} - 2 x - 3$	$37$	[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...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	$2$	$18$
37.3.200...112.1	$x^{37} - 4 x - 2$	$37$	[3,17]	$-\,2^{36}\cdot 1181\cdot 156768103\cdot 3595021207\cdot 43\!\cdots\!67$	$5$	$130.707426027$	$1.0614730718773003e+34$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$19$
37.3.200...107.1	$x^{37} - 4 x - 1$	$37$	[3,17]	$-\,53\cdot 139\cdot 27\!\cdots\!21$	$3$	$130.707426029$	$1.4176037499701838e+39$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$19$
37.1.200...136.1	$x^{37} + 4 x - 2$	$37$	[1,18]	$2^{36}\cdot 249494962454898495919\cdot 11\!\cdots\!79$	$3$	$130.70742603$	$1.0614730722604274e+34$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.201...181.1	$x^{37} + 4 x - 3$	$37$	[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	$x^{37} - 2 x - 4$	$37$	[1,18]	$2^{70}\cdot 5\cdot 7\cdot 47\cdot 64\!\cdots\!17$	$5$	$137.314984457$				?	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.124...256.1	$x^{37} + 2 x - 4$	$37$	[1,18]	$2^{70}\cdot 13\cdot 137\cdot 195791\cdot 10489284688357\cdot 5723750340436657\cdot 504174169295944373011$	$7$	$137.314984457$				?	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.498...464.1	$x^{37} - 3 x - 4$	$37$	[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	$x^{37} + 5 x - 3$	$37$	[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	$x^{37} + 5 x - 2$	$37$	[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	$x^{37} - 5 x - 3$	$37$	[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	$x^{37} + 5 x - 1$	$37$	[1,18]	$7\cdot 47\cdot 23\!\cdots\!73$	$3$	$163.384282536$	$8.798124312680973e+40$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.779...832.1	$x^{37} + 5 x - 4$	$37$	[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	$x^{37} - 5 x - 5$	$37$	[1,18]	$5^{36}\cdot 563\cdot 175944697081\cdot 746724389353\cdot 13\!\cdots\!43$	$5$	$176.877946858$	$4.792720264945012e+29$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.153...501.1	$x^{37} - 4 x - 5$	$37$	[1,18]	$15\!\cdots\!01$	$1$	$177.125257097$	$3.919125151102706e+41$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.153...757.1	$x^{37} - 3 x - 5$	$37$	[1,18]	$47\cdot 4458653\cdot 39030547\cdot 4191145897\cdot 2748399402101\cdot 46040166590110289\cdot 35410190689086361595487217777$	$7$	$177.125319729$	$3.91915078878761e+41$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.153...933.1	$x^{37} - 2 x - 5$	$37$	[1,18]	$7\cdot 34591\cdot 96167\cdot 163386011\cdot 40\!\cdots\!57$	$5$	$177.12531973$	$3.9191507893987696e+41$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.153...989.1	$x^{37} - x - 5$	$37$	[1,18]	$11\cdot 107\cdot 359\cdot 60013\cdot 22231407377\cdot 27\!\cdots\!23$	$6$	$177.12531973$	$3.9191507893987696e+41$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$
37.1.161...125.1	$x^{37} + 5 x - 5$	$37$	[1,18]	$5^{36}\cdot 7\cdot 17\cdot 39619\cdot 50081864423\cdot 2601293855703705209\cdot 18050801224775844479711$	$7$	$177.360848235$	$5.040659391404967e+29$			✓	$S_{37}$ (as 37T11)	not computed	$2$	$18$

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