Number field search results

Results (1-50 of 2553120 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
2.0.3.1	$x^{2} - x + 1$	$2$	[0,1]	$-\,3$	$1$	$1.73205080757$	$1.7320508075688772$	✓	✓	✓	$C_2$ (as 2T1)	trivial	$6$	0	$1$
2.2.24.1	$x^{2} - 6$	$2$	[2,0]	$2^{3}\cdot 3$	$2$	$4.89897948557$	$4.898979485566356$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$2.29243166956$
2.2.33.1	$x^{2} - x - 8$	$2$	[2,0]	$3\cdot 11$	$2$	$5.74456264654$	$5.744562646538029$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.82816847133$
2.0.39.1	$x^{2} - x + 10$	$2$	[0,1]	$-\,3\cdot 13$	$2$	$6.2449979984$	$6.244997998398398$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	0	$1$
2.2.60.1	$x^{2} - 15$	$2$	[2,0]	$2^{2}\cdot 3\cdot 5$	$3$	$7.74596669241$	$7.745966692414834$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.0634370689$
2.2.69.1	$x^{2} - x - 17$	$2$	[2,0]	$3\cdot 23$	$2$	$8.30662386292$	$8.306623862918075$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$3.21727197116$
2.0.84.1	$x^{2} + 21$	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 7$	$3$	$9.16515138991$	$9.16515138991168$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	0	$1$
2.2.105.1	$x^{2} - x - 26$	$2$	[2,0]	$3\cdot 5\cdot 7$	$3$	$10.246950766$	$10.246950765959598$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.40657049308$
2.0.111.1	$x^{2} - x + 28$	$2$	[0,1]	$-\,3\cdot 37$	$2$	$10.5356537529$	$10.535653752852738$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	0	$1$
2.0.120.1	$x^{2} + 30$	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 5$	$3$	$10.9544511501$	$10.954451150103322$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	0	$1$
2.2.141.1	$x^{2} - x - 35$	$2$	[2,0]	$3\cdot 47$	$2$	$11.874342087$	$11.874342087037917$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$5.24699637018$
2.2.168.1	$x^{2} - 42$	$2$	[2,0]	$2^{3}\cdot 3\cdot 7$	$3$	$12.9614813968$	$12.96148139681572$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$3.2566139548$
2.2.177.1	$x^{2} - x - 44$	$2$	[2,0]	$3\cdot 59$	$2$	$13.3041346957$	$13.30413469565007$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$11.7348362567$
2.0.183.1	$x^{2} - x + 46$	$2$	[0,1]	$-\,3\cdot 61$	$2$	$13.5277492585$	$13.527749258468683$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	0	$1$
2.2.204.1	$x^{2} - 51$	$2$	[2,0]	$2^{2}\cdot 3\cdot 17$	$3$	$14.2828568571$	$14.2828568570857$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.60507017098$
2.2.213.1	$x^{2} - x - 53$	$2$	[2,0]	$3\cdot 71$	$2$	$14.5945195193$	$14.594519519326424$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$4.29027173584$
2.0.219.1	$x^{2} - x + 55$	$2$	[0,1]	$-\,3\cdot 73$	$2$	$14.7986485869$	$14.798648586948742$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	0	$1$
2.0.228.1	$x^{2} + 57$	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 19$	$3$	$15.0996688705$	$15.0996688705415$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	0	$1$
2.2.249.1	$x^{2} - x - 62$	$2$	[2,0]	$3\cdot 83$	$2$	$15.7797338381$	$15.7797338380595$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$16.6550351208$
2.0.255.1	$x^{2} - x + 64$	$2$	[0,1]	$-\,3\cdot 5\cdot 17$	$3$	$15.9687194227$	$15.968719422671311$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 6]$	$2$	0	$1$
2.0.264.1	$x^{2} + 66$	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 11$	$3$	$16.2480768093$	$16.24807680927192$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	0	$1$
2.2.285.1	$x^{2} - x - 71$	$2$	[2,0]	$3\cdot 5\cdot 19$	$3$	$16.8819430161$	$16.881943016134134$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.82973503752$
2.0.291.1	$x^{2} - x + 73$	$2$	[0,1]	$-\,3\cdot 97$	$2$	$17.0587221092$	$17.05872210923198$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	0	$1$
2.2.312.1	$x^{2} - 78$	$2$	[2,0]	$2^{3}\cdot 3\cdot 13$	$3$	$17.6635217327$	$17.663521732655695$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.66335008258$
2.2.321.1	$x^{2} - x - 80$	$2$	[2,0]	$3\cdot 107$	$2$	$17.9164728672$	$17.916472867168917$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$6.06377980031$
2.0.327.1	$x^{2} - x + 82$	$2$	[0,1]	$-\,3\cdot 109$	$2$	$18.08314132$	$18.083141320025124$	✓	✓	✓	$C_2$ (as 2T1)	$[12]$	$2$	0	$1$
2.2.348.1	$x^{2} - 87$	$2$	[2,0]	$2^{2}\cdot 3\cdot 29$	$3$	$18.6547581062$	$18.65475810617763$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.02503266055$
2.2.357.1	$x^{2} - x - 89$	$2$	[2,0]	$3\cdot 7\cdot 17$	$3$	$18.8944436277$	$18.894443627691185$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$2.94165731465$
2.0.372.1	$x^{2} + 93$	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 31$	$3$	$19.287301522$	$19.28730152198591$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	0	$1$
2.2.393.1	$x^{2} - x - 98$	$2$	[2,0]	$3\cdot 131$	$2$	$19.8242276016$	$19.82422760159901$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$18.3467573732$
2.0.399.1	$x^{2} - x + 100$	$2$	[0,1]	$-\,3\cdot 7\cdot 19$	$3$	$19.9749843554$	$19.974984355438178$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 8]$	$2$	0	$1$
2.0.408.1	$x^{2} + 102$	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 17$	$3$	$20.1990098767$	$20.199009876724155$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	0	$1$
2.2.429.1	$x^{2} - x - 107$	$2$	[2,0]	$3\cdot 11\cdot 13$	$3$	$20.7123151772$	$20.71231517720798$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.9766861766$
2.0.435.1	$x^{2} - x + 109$	$2$	[0,1]	$-\,3\cdot 5\cdot 29$	$3$	$20.8566536146$	$20.85665361461421$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	0	$1$
2.2.456.1	$x^{2} - 114$	$2$	[2,0]	$2^{3}\cdot 3\cdot 19$	$3$	$21.3541565041$	$21.354156504062622$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$7.62559483418$
2.2.465.1	$x^{2} - x - 116$	$2$	[2,0]	$3\cdot 5\cdot 31$	$3$	$21.5638586528$	$21.563858652847824$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$10.3653960031$
2.0.471.1	$x^{2} - x + 118$	$2$	[0,1]	$-\,3\cdot 157$	$2$	$21.7025344142$	$21.702534414210707$	✓	✓	✓	$C_2$ (as 2T1)	$[16]$	$2$	0	$1$
2.2.492.1	$x^{2} - 123$	$2$	[2,0]	$2^{2}\cdot 3\cdot 41$	$3$	$22.1810730128$	$22.181073012818835$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$5.49715142831$
2.2.501.1	$x^{2} - x - 125$	$2$	[2,0]	$3\cdot 167$	$2$	$22.3830292856$	$22.38302928559939$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$10.2479633878$
2.0.516.1	$x^{2} + 129$	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 43$	$3$	$22.7156333832$	$22.715633383201094$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 6]$	$2$	0	$1$
2.2.537.1	$x^{2} - x - 134$	$2$	[2,0]	$3\cdot 179$	$2$	$23.1732604525$	$23.173260452512935$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$19.7679715759$
2.0.543.1	$x^{2} - x + 136$	$2$	[0,1]	$-\,3\cdot 181$	$2$	$23.3023603955$	$23.302360395462088$	✓	✓	✓	$C_2$ (as 2T1)	$[12]$	$2$	0	$1$
2.0.552.1	$x^{2} + 138$	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 23$	$3$	$23.4946802489$	$23.49468024894146$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	0	$1$
2.2.573.1	$x^{2} - x - 143$	$2$	[2,0]	$3\cdot 191$	$2$	$23.9374184072$	$23.93741840717165$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$6.64118046545$
2.0.579.1	$x^{2} - x + 145$	$2$	[0,1]	$-\,3\cdot 193$	$2$	$24.062418831$	$24.06241883103193$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	0	$1$
2.2.609.1	$x^{2} - x - 152$	$2$	[2,0]	$3\cdot 7\cdot 29$	$3$	$24.6779253585$	$24.677925358506133$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$14.0072790186$
2.0.615.1	$x^{2} - x + 154$	$2$	[0,1]	$-\,3\cdot 5\cdot 41$	$3$	$24.7991935353$	$24.79919353527449$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	0	$1$
2.2.636.1	$x^{2} - 159$	$2$	[2,0]	$2^{2}\cdot 3\cdot 53$	$3$	$25.2190404258$	$25.219040425836983$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$7.88155977444$
2.2.645.1	$x^{2} - x - 161$	$2$	[2,0]	$3\cdot 5\cdot 43$	$3$	$25.3968501984$	$25.39685019840059$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$4.84412508057$
2.0.651.1	$x^{2} - x + 163$	$2$	[0,1]	$-\,3\cdot 7\cdot 31$	$3$	$25.5147016443$	$25.514701644346147$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	0	$1$

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