Number field search results

Note: Search results may be incomplete due to uncomputed quantities: local_algs (140954 objects)

Degree	Signature	Class number	Class group structure	CM field
Ramified prime count	Ramified	Unramified primes	Galois group	Is Galois
Discriminant	Root discriminant	Regulator	Intermediate field	$p$-adic completions
Monogenic	Index	Ines. \(p\)

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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
2.0.71.1	x^2 - x + 18	$2$	[0,1]	$-\,71$	$1$	$8.42614977318$	✓	✓	✓	$C_2$ (as 2T1)	$[7]$	$2$	$0$	$1$
2.0.355.1	x^2 - x + 89	$2$	[0,1]	$-\,5\cdot 71$	$2$	$18.8414436814$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.2.497.1	x^2 - x - 124	$2$	[2,0]	$7\cdot 71$	$2$	$22.2934968096$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$14.6925505602$
2.0.568.1	x^2 + 142	$2$	[0,1]	$-\,2^{3}\cdot 71$	$2$	$23.8327505756$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.2.781.1	x^2 - x - 195	$2$	[2,0]	$11\cdot 71$	$2$	$27.946377225$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$18.7223574186$
2.0.852.1	x^2 + 213	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 71$	$3$	$29.1890390387$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.2.1633.1	x^2 - x - 408	$2$	[2,0]	$23\cdot 71$	$2$	$40.4103947024$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$54.8465061829$
2.0.1704.1	x^2 + 426	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 71$	$3$	$41.2795348811$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 12]$	$2$	$0$	$1$
2.0.2059.1	x^2 - x + 515	$2$	[0,1]	$-\,29\cdot 71$	$2$	$45.3762052182$	✓	✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$0$	$1$
2.2.2201.1	x^2 - x - 550	$2$	[2,0]	$31\cdot 71$	$2$	$46.914816423$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$45.2783229375$
2.2.2485.1	x^2 - x - 621	$2$	[2,0]	$5\cdot 7\cdot 71$	$3$	$49.8497743225$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$11.2556691326$
2.0.2627.1	x^2 - x + 657	$2$	[0,1]	$-\,37\cdot 71$	$2$	$51.254268115$	✓	✓	✓	$C_2$ (as 2T1)	$[12]$	$2$	$0$	$1$
2.2.2769.1	x^2 - x - 692	$2$	[2,0]	$3\cdot 13\cdot 71$	$3$	$52.6212884677$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$34.1774715812$
2.0.2840.1	x^2 + 710	$2$	[0,1]	$-\,2^{3}\cdot 5\cdot 71$	$3$	$53.2916503779$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 16]$	$2$	$0$	$1$
2.2.3337.1	x^2 - x - 834	$2$	[2,0]	$47\cdot 71$	$2$	$57.7667724561$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$69.7693940715$
2.2.3621.1	x^2 - x - 905	$2$	[2,0]	$3\cdot 17\cdot 71$	$3$	$60.1747455333$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$13.6475592527$
2.2.3692.1	x^2 - 923	$2$	[2,0]	$2^{2}\cdot 13\cdot 71$	$3$	$60.7618301239$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$7.15148484972$
2.2.3905.1	x^2 - x - 976	$2$	[2,0]	$5\cdot 11\cdot 71$	$3$	$62.4899991999$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$9.43332390409$
2.2.3976.1	x^2 - 994	$2$	[2,0]	$2^{3}\cdot 7\cdot 71$	$3$	$63.0555310817$		✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$1$	$7.72753491641$
2.0.4047.1	x^2 - x + 1012	$2$	[0,1]	$-\,3\cdot 19\cdot 71$	$3$	$63.6160357143$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 20]$	$2$	$0$	$1$
2.2.4189.1	x^2 - x - 1047	$2$	[2,0]	$59\cdot 71$	$2$	$64.7224845011$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$41.962146063$
2.0.4260.1	x^2 + 1065	$2$	[0,1]	$-\,2^{2}\cdot 3\cdot 5\cdot 71$	$4$	$65.2686754883$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2, 4]$	$2$	$0$	$1$
2.2.4757.1	x^2 - x - 1189	$2$	[2,0]	$67\cdot 71$	$2$	$68.9710084021$		✓	✓	$C_2$ (as 2T1)	$[5]$	$2$	$1$	$4.23389639848$
2.2.4828.1	x^2 - 1207	$2$	[2,0]	$2^{2}\cdot 17\cdot 71$	$3$	$69.4838110642$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$14.6570156728$
2.0.5183.1	x^2 - x + 1296	$2$	[0,1]	$-\,71\cdot 73$	$2$	$71.9930552206$	✓	✓	✓	$C_2$ (as 2T1)	$[80]$	$2$	$0$	$1$
2.0.5396.1	x^2 + 1349	$2$	[0,1]	$-\,2^{2}\cdot 19\cdot 71$	$3$	$73.4574706888$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 28]$	$2$	$0$	$1$
2.0.5467.1	x^2 - x + 1367	$2$	[0,1]	$-\,7\cdot 11\cdot 71$	$3$	$73.9391641825$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.2.5964.1	x^2 - 1491	$2$	[2,0]	$2^{2}\cdot 3\cdot 7\cdot 71$	$4$	$77.2269383052$		✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$1$	$11.8237868103$
2.2.6248.1	x^2 - 1562	$2$	[2,0]	$2^{3}\cdot 11\cdot 71$	$3$	$79.0442913815$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$15.1037493241$
2.0.6319.1	x^2 - x + 1580	$2$	[0,1]	$-\,71\cdot 89$	$2$	$79.492137976$	✓	✓	✓	$C_2$ (as 2T1)	$[52]$	$2$	$0$	$1$
2.0.7171.1	x^2 - x + 1793	$2$	[0,1]	$-\,71\cdot 101$	$2$	$84.6817571854$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$0$	$1$
2.2.7384.1	x^2 - 1846	$2$	[2,0]	$2^{3}\cdot 13\cdot 71$	$3$	$85.9302042358$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$37.0707285905$
2.0.7739.1	x^2 - x + 1935	$2$	[0,1]	$-\,71\cdot 109$	$2$	$87.9715863219$	✓	✓	✓	$C_2$ (as 2T1)	$[40]$	$2$	$0$	$1$
2.2.8165.1	x^2 - x - 2041	$2$	[2,0]	$5\cdot 23\cdot 71$	$3$	$90.3603895521$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$10.9270529666$
2.0.8520.1	x^2 + 2130	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 5\cdot 71$	$4$	$92.3038460737$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 2, 8]$	$2$	$0$	$1$
2.2.8733.1	x^2 - x - 2183	$2$	[2,0]	$3\cdot 41\cdot 71$	$3$	$93.4505216679$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$14.7803518062$
2.2.9017.1	x^2 - x - 2254	$2$	[2,0]	$71\cdot 127$	$2$	$94.9578854019$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$59.8580642674$
2.0.9159.1	x^2 - x + 2290	$2$	[0,1]	$-\,3\cdot 43\cdot 71$	$3$	$95.7026645397$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 48]$	$2$	$0$	$1$
2.2.9372.1	x^2 - 2343	$2$	[2,0]	$2^{2}\cdot 3\cdot 11\cdot 71$	$4$	$96.8090904822$		✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$1$	$9.96636844837$
2.2.9656.1	x^2 - 2414	$2$	[2,0]	$2^{3}\cdot 17\cdot 71$	$3$	$98.2649479723$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$26.0224446373$
2.2.9869.1	x^2 - x - 2467	$2$	[2,0]	$71\cdot 139$	$2$	$99.3428407083$		✓	✓	$C_2$ (as 2T1)	$[3]$	$2$	$1$	$8.15392504929$
2.0.10295.1	x^2 - x + 2574	$2$	[0,1]	$-\,5\cdot 29\cdot 71$	$3$	$101.464279429$	✓	✓	✓	$C_2$ (as 2T1)	$[4, 32]$	$2$	$0$	$1$
2.0.10792.1	x^2 + 2698	$2$	[0,1]	$-\,2^{3}\cdot 19\cdot 71$	$3$	$103.884551306$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 12]$	$2$	$0$	$1$
2.2.11005.1	x^2 - x - 2751	$2$	[2,0]	$5\cdot 31\cdot 71$	$3$	$104.904718674$		✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$1$	$7.69757514075$
2.0.11147.1	x^2 - x + 2787	$2$	[0,1]	$-\,71\cdot 157$	$2$	$105.579354042$	✓	✓	✓	$C_2$ (as 2T1)	$[28]$	$2$	$0$	$1$
2.2.11289.1	x^2 - x - 2822	$2$	[2,0]	$3\cdot 53\cdot 71$	$3$	$106.249705882$		✓	✓	$C_2$ (as 2T1)	$[18]$	$2$	$1$	$6.7452349654$
2.0.11431.1	x^2 - x + 2858	$2$	[0,1]	$-\,7\cdot 23\cdot 71$	$3$	$106.915854764$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 40]$	$2$	$0$	$1$
2.2.11573.1	x^2 - x - 2893	$2$	[2,0]	$71\cdot 163$	$2$	$107.577878767$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$31.1247892807$
2.2.11644.1	x^2 - 2911	$2$	[2,0]	$2^{2}\cdot 41\cdot 71$	$3$	$107.907367682$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$49.5298936845$
2.2.11928.1	x^2 - 2982	$2$	[2,0]	$2^{3}\cdot 3\cdot 7\cdot 71$	$4$	$109.215383532$		✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$1$	$9.56085638364$

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