Number field search results

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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Results (1-50 of 2828513 matches)

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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
10.0.209352647.1	x^10 - 3x^9 + 7x^8 - 11x^7 + 13x^6 - 12x^5 + 9x^4 - 5x^3 + 3x^2 - 2x + 1	$10$	[0,5]	$-\,7^{2}\cdot 23\cdot 431^{2}$	$$	$6.79341030426$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.568036883757$
10.0.212309359.1	x^10 - 3x^9 + 5x^8 - 7x^7 + 9x^6 - 10x^5 + 9x^4 - 7x^3 + 5x^2 - 2x + 1	$10$	[0,5]	$-\,31\cdot 2617^{2}$	$$	$6.80294428088$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.572857558707$
10.0.214816879.1	x^10 - 2x^9 + 4x^8 - 7x^7 + 9x^6 - 10x^5 + 10x^4 - 8x^3 + 6x^2 - 3x + 1	$10$	[0,5]	$-\,17^{2}\cdot 79\cdot 97^{2}$	$$	$6.81093664096$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.577674891408$
10.0.215067767.1	x^10 - x^9 - x^8 + 2x^7 + x^6 - 3x^5 + 3x^3 - x^2 - x + 1	$10$	[0,5]	$-\,215067767$	$$	$6.81173168317$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.5781462354099604$
10.0.216670707.1	x^10 - 3x^9 + 5x^8 - 6x^7 + 6x^6 - 4x^5 + 2x^4 - x^3 + x^2 - x + 1	$10$	[0,5]	$-\,3^{5}\cdot 11^{2}\cdot 7369$	$$	$6.8167916456$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$1.74293786533$
10.0.220168975.1	x^10 - x^9 - x^8 + 2x^7 - x^6 - x^5 + 4x^4 - x^3 - 3x^2 + x + 1	$10$	[0,5]	$-\,5^{2}\cdot 13^{2}\cdot 31\cdot 41^{2}$	$$	$6.82771857501$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.586605631071$
10.0.220506347.1	x^10 - 3x^9 + 5x^8 - 5x^7 + 3x^6 - x^4 + x^3 - x + 1	$10$	[0,5]	$-\,37\cdot 677\cdot 8803$	$$	$6.82876408755$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.5880175904588231$
10.0.224198759.1	x^10 - x^9 - 2x^8 + 4x^7 - 4x^5 + 3x^4 + x^3 - 2x^2 + 1	$10$	[0,5]	$-\,71\cdot 1777^{2}$	$$	$6.84011369338$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.59340069383$
10.0.224415603.1	x^10 + 2x^8 - 3x^7 + 3x^6 - 7x^5 + 8x^4 - 7x^3 + 7x^2 - 4x + 1	$10$	[0,5]	$-\,3^{5}\cdot 31^{4}$	$$	$6.84077497824$			✓	$D_5\times C_5$ (as 10T6)	trivial	$6$	$4$	$1.78149530531$
10.0.226173952.1	x^10 - x^8 - 2x^7 - x^6 + 2x^5 + 2x^4 - x^2 + 1	$10$	[0,5]	$-\,2^{10}\cdot 220873$	$$	$6.84611608122$			not computed	$S_5^2 \wr C_2$ (as 10T43)	trivial	$4$	$4$	$1.19443787527$
10.0.226876987.1	x^10 - 2x^9 + 3x^8 - 3x^7 + 2x^6 + x^5 - x^4 - 3x^3 + 6x^2 - 4x + 1	$10$	[0,5]	$-\,43\cdot 2297^{2}$	$$	$6.8482411447$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.597809920275$
10.0.227991979.1	x^10 - x^9 - x^8 + 3x^7 - x^6 - 3x^5 + 3x^4 + x^3 - 2x^2 + 1	$10$	[0,5]	$-\,599\cdot 380621$	$$	$6.85159930803$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.5998219105603662$
10.0.229203619.1	x^10 - x^9 + 2x^8 - 3x^7 + 4x^6 - 4x^5 + 4x^4 - 4x^3 + 3x^2 - 2x + 1	$10$	[0,5]	$-\,229203619$	$$	$6.85523184156$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6020080437571057$
10.0.229345007.1	x^10 - x^9 + 6x^8 - 3x^7 + 11x^6 - 3x^5 + 11x^4 - 3x^3 + 6x^2 - x + 1	$10$	[0,5]	$-\,47^{5}$	$$	$6.8556546004$		✓	not computed	$D_5$ (as 10T2)	trivial	$2$	$4$	$0.60186322759$
10.0.233043179.1	x^10 - x^9 + 2x^8 - 4x^7 + 4x^6 - 5x^5 + 5x^4 - 4x^3 + 3x^2 - x + 1	$10$	[0,5]	$-\,97\cdot 463\cdot 5189$	$$	$6.86662988937$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6084964369407401$
10.0.236184579.1	x^10 - 3x^9 + 5x^8 - 7x^7 + 7x^6 - 6x^5 + 4x^4 - 2x^3 + x^2 + 1	$10$	[0,5]	$-\,3^{5}\cdot 37\cdot 109\cdot 241$	$$	$6.87583036876$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$1.84211740914$
10.0.236438047.1	x^10 - 2x^9 + x^8 + 2x^7 - 3x^6 + x^5 + x^4 - x + 1	$10$	[0,5]	$-\,236438047$	$$	$6.87656791137$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.614960446273$
10.0.240232739.1	x^10 - 2x^9 + 2x^8 - 2x^6 + 4x^5 - 4x^4 + x^3 + 3x^2 - 3x + 1	$10$	[0,5]	$-\,467\cdot 514417$	$$	$6.88752549237$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.622824662223$
10.0.243226747.1	x^10 - 3x^9 + 4x^8 - 3x^7 + 2x^6 - x^5 + x^4 - 2x^3 + 3x^2 - 2x + 1	$10$	[0,5]	$-\,243226747$	$$	$6.89606161454$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6261475736016512$
10.0.243415027.1	x^10 - x^7 + x^6 + 2x^5 - x^3 - 2x^2 + 1	$10$	[0,5]	$-\,17\cdot 14318531$	$$	$6.89659524764$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6267229276822098$
10.0.244175707.1	x^10 - x^9 + x^7 - x^6 - x^4 + x^3 + x^2 - x + 1	$10$	[0,5]	$-\,19^{2}\cdot 676387$	$$	$6.89874743162$			not computed	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6277987643994235$
10.0.246071287.1	x^10 - 3x^9 + 7x^8 - 12x^7 + 15x^6 - 15x^5 + 12x^4 - 7x^3 + 4x^2 - 2x + 1	$10$	[0,5]	$-\,7^{5}\cdot 11^{4}$	$$	$6.90408443551$			✓	$D_5\times C_5$ (as 10T6)	trivial	$2$	$4$	$0.634803768223$
10.0.246944619.1	x^10 - x^9 + x^6 - x^5 - x^4 + 3x^3 - x^2 - x + 1	$10$	[0,5]	$-\,3^{5}\cdot 73\cdot 13921$	$$	$6.90653086059$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$1.90076515959$
10.0.250679267.1	x^10 - x^9 - 2x^8 + x^7 + 3x^6 - 2x^4 - 2x^3 + 2x + 1	$10$	[0,5]	$-\,250679267$	$$	$6.91690548889$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6409749870444131$
10.0.252486127.1	x^10 - x^9 + 2x^8 - 4x^7 + 4x^6 - 4x^5 + 5x^4 - 3x^3 + 2x^2 - 2x + 1	$10$	[0,5]	$-\,787\cdot 320821$	$$	$6.92187499705$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.642537334981687$
10.0.254121139.1	x^10 - 2x^8 - x^7 + 2x^6 + 3x^5 - 3x^3 - x^2 + x + 1	$10$	[0,5]	$-\,149\cdot 991\cdot 1721$	$$	$6.92634435313$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6480210196495108$
10.0.260270739.1	x^10 - x^8 - 2x^7 + x^6 + 3x^5 - 2x^4 - 4x^3 + x^2 + 3x + 1	$10$	[0,5]	$-\,3^{5}\cdot 163\cdot 6571$	$$	$6.9429259695$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$1.96704129047$
10.0.262091507.1	x^10 - x^9 - 2x^6 + 3x^5 + 3x^4 - 4x^3 - 2x^2 + 2x + 1	$10$	[0,5]	$-\,83\cdot 1777^{2}$	$$	$6.94776778804$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.656821013577$
10.0.262477979.1	x^10 - x^9 + x^8 - 2x^6 + x^5 - x^4 + x^2 + 1	$10$	[0,5]	$-\,251\cdot 1045729$	$$	$6.94879160514$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6577090020502393$
10.0.262864627.1	x^10 - 2x^8 - x^7 + x^6 + 2x^5 - x^4 - 2x^3 + x^2 + x + 1	$10$	[0,5]	$-\,353\cdot 744659$	$$	$6.94981453173$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6619032898743505$
10.0.262909719.1	x^10 - x^8 - x^7 - 2x^6 + 4x^4 + x^3 - 2x^2 + 1	$10$	[0,5]	$-\,3^{5}\cdot 73\cdot 14821$	$$	$6.94993374018$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$1.97569183141$
10.0.263786699.1	x^10 - 2x^9 + 2x^8 - 2x^7 + 4x^6 - 5x^5 + 4x^4 - 2x^3 + 3x^2 - 3x + 1	$10$	[0,5]	$-\,11\cdot 59^{2}\cdot 83^{2}$	$$	$6.95224853606$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.663236848943$
10.0.268043264.1	x^10 - 2x^9 + 3x^8 - 6x^7 + 6x^6 - 6x^5 + 7x^4 - 4x^3 + 3x^2 - 2x + 1	$10$	[0,5]	$-\,2^{10}\cdot 261761$	$$	$6.96338631704$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$4$	$4$	$1.33676061738$
10.0.274127275.1	x^10 - x^9 + x^8 - 3x^7 + 3x^6 - x^5 + 3x^4 - 3x^3 + 1	$10$	[0,5]	$-\,5^{2}\cdot 59\cdot 185849$	$$	$6.9790325665$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6754062116693342$
10.0.274550779.1	x^10 - x^9 + 2x^8 - 2x^7 + 3x^6 - 3x^5 + 3x^4 - 3x^3 + 2x^2 - 2x + 1	$10$	[0,5]	$-\,19\cdot 14450041$	$$	$6.98011002054$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6811521995711005$
10.0.277010267.1	x^10 - 2x^9 + x^8 + 2x^7 - 3x^6 + 3x^5 - 2x^4 + 3x^2 - 3x + 1	$10$	[0,5]	$-\,107\cdot 1609^{2}$	$$	$6.98633789626$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.679993136866$
10.0.278005859.1	x^10 - x^9 - x^8 + 4x^7 - 2x^6 - 3x^5 + 4x^4 - 2x^2 + 1	$10$	[0,5]	$-\,278005859$	$$	$6.98884477745$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6840713547835329$
10.0.278645219.1	x^10 + 3x^8 - x^7 + 4x^6 - x^5 + 4x^4 + 2x^2 + 1	$10$	[0,5]	$-\,317\cdot 879007$	$$	$6.99045041632$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6850935429811508$
10.0.281268947.1	x^10 + 3x^8 - x^7 + 4x^6 - x^5 + 4x^4 - x^3 + 2x^2 - x + 1	$10$	[0,5]	$-\,281268947$	$$	$6.99700491098$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6911023529825022$
10.0.282748447.1	x^10 - x^9 - 2x^8 + 3x^7 + 2x^6 - 5x^5 + x^4 + 4x^3 - 2x^2 - x + 1	$10$	[0,5]	$-\,282748447$	$$	$7.00067671564$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.689666096131428$
10.0.283885691.1	x^10 - x^9 + 2x^8 - 4x^7 + 3x^6 - 4x^5 + 3x^4 - 2x^3 + 2x^2 + 1	$10$	[0,5]	$-\,8941\cdot 31751$	$$	$7.00348737806$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6905689191175234$
10.0.284152779.1	x^10 - x^9 - 2x^8 + 3x^7 + 2x^6 - 3x^5 - 2x^4 + 3x^3 + x^2 - 2x + 1	$10$	[0,5]	$-\,3^{5}\cdot 1169353$	$$	$7.00414600793$			✓	$S_5^2 \wr C_2$ (as 10T43)	trivial	$6$	$4$	$2.07998415618$
10.0.285267739.1	x^10 - x^9 + x^8 - x^7 - x^5 + 3x^4 - 4x^3 + 4x^2 - 2x + 1	$10$	[0,5]	$-\,285267739$	$$	$7.00688945735$			not computed	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.6944480441748214$
10.0.288806267.1	x^10 - x^9 - x^8 + 2x^7 - x^5 + x^3 - x + 1	$10$	[0,5]	$-\,1321\cdot 218627$	$$	$7.01553283007$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.7003014151706757$
10.0.290432899.1	x^10 - 3x^8 - x^7 + 4x^6 + 3x^5 - 2x^4 - 4x^3 + 2x + 1	$10$	[0,5]	$-\,89\cdot 3263291$	$$	$7.01947418146$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.7058632532986308$
10.0.290491759.1	x^10 - 3x^9 + 5x^8 - 5x^7 + 5x^6 - 6x^5 + 6x^4 - 3x^3 + x^2 - x + 1	$10$	[0,5]	$-\,290491759$	$$	$7.01961642725$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.7034426859963029$
10.0.290954507.1	x^10 - x^9 + 2x^8 + 2x^7 - x^6 + 4x^5 + 4x^4 + 2x^2 + 3x + 1	$10$	[0,5]	$-\,17^{2}\cdot 97^{2}\cdot 107$	$$	$7.02073383839$			✓	$C_2 \wr S_5$ (as 10T39)	trivial	$2$	$4$	$0.702250275284$
10.0.291458939.1	x^10 - x^9 + 2x^8 - 2x^6 + 3x^5 - 3x^4 + 2x^2 - 2x + 1	$10$	[0,5]	$-\,197\cdot 1479487$	$$	$7.02195008451$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.7047631819012555$
10.0.292693979.1	x^10 - 3x^9 + 4x^8 - 3x^7 + 3x^6 - 4x^5 + 3x^4 - x + 1	$10$	[0,5]	$-\,127\cdot 239\cdot 9643$	$$	$7.02491993562$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.7063782727510773$
10.0.293025059.1	x^10 - 2x^9 + 3x^8 - 4x^7 + 5x^6 - 6x^5 + 8x^4 - 8x^3 + 6x^2 - 3x + 1	$10$	[0,5]	$-\,293025059$	$$	$7.02571415335$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$0.7066552938338644$

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