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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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
10.2.4165509529.1	x^10 - x^9 - x^8 + 3x^7 - 2x^6 - x^5 + 3x^4 - x^2 - x + 1	$10$	[2,4]	$1609^{3}$	$$	$9.16150479476$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$4.78851392314$
10.2.4483962449.1	x^10 - x^7 - x^5 + x^4 - 2x^3 + x^2 - x + 1	$10$	[2,4]	$17^{3}\cdot 97^{3}$	$$	$9.22924546222$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$5.90538181209$
10.2.5441006848.2	x^10 - x^8 - 4x^7 + 2x^6 - 2x^5 + 4x^4 - 4x^3 + x^2 - 2x + 1	$10$	[2,4]	$2^{8}\cdot 277^{3}$	$$	$9.40952991361$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$6.62426511052$
10.2.5611284433.1	x^10 - x^9 + x^8 - 2x^7 + x^6 + x^5 - 4x^4 + 3x^3 - 2x + 1	$10$	[2,4]	$1777^{3}$	$$	$9.43857059288$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$5.80208478511$
10.2.10882188544.1	x^10 - x^8 - 2x^7 - 2x^6 - 4x^5 + 2x^3 + x^2 + 1	$10$	[2,4]	$2^{8}\cdot 349^{3}$	$$	$10.0849006602$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$9.09322598856$
10.2.12119452073.2	x^10 - x^9 + x^8 - x^6 - x^5 + x^3 - x^2 - x + 1	$10$	[2,4]	$2297^{3}$	$$	$10.1940861283$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$10.5649221834$
10.2.17923019113.1	x^10 - x^9 - 4x^7 + 2x^6 + 2x^5 + x^4 - x^3 - 2x + 1	$10$	[2,4]	$2617^{3}$	$$	$10.6008604331$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$9.83053678535$
10.2.18927429625.1	x^10 - x^9 - x^8 + 2x^7 - 3x^6 - x^5 + 4x^4 - x^3 + x^2 - x + 1	$10$	[2,4]	$5^{3}\cdot 13^{3}\cdot 41^{3}$	$$	$10.6588208799$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$11.5338423415$
10.2.23615200909.3	x^10 + x^8 - x^6 - 2x^5 - x^4 - x^3 + 1	$10$	[2,4]	$19^{3}\cdot 151^{3}$	$$	$10.8973064585$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$22.3279296286$
10.2.25080878336.1	x^10 - x^9 - x^8 + 2x^7 + 3x^6 + 3x^5 - 5x^4 - 12x^3 - 11x^2 - 5x - 1	$10$	[2,4]	$2^{8}\cdot 461^{3}$	$$	$10.9631226838$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$18.76633546$
10.2.27461605913.1	x^10 - x^7 - x^6 - 2x^5 + x + 1	$10$	[2,4]	$7^{3}\cdot 431^{3}$	$$	$11.0629918653$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$17.7848312304$
10.2.29474993969.1	x^10 - x^9 - 2x^8 + 4x^7 - 4x^6 - 2x^5 + 7x^4 - x^3 - 2x^2 + 1	$10$	[2,4]	$3089^{3}$	$$	$11.1415438144$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$14.0762389296$
10.2.33608047921.1	x^10 - 3x^8 + 2x^6 - 2x^5 + 5x^4 + 4x^3 - 3x^2 - 4x - 1	$10$	[2,4]	$7^{4}\cdot 241^{3}$	$$	$11.2887103211$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$18.676897024$
10.2.33792250337.1	x^10 - x^7 + x^6 - 2x^5 - x + 1	$10$	[2,4]	$53^{3}\cdot 61^{3}$	$$	$11.2948823451$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$18.5117480209$
10.2.38238692409.1	x^10 - x^9 + x^8 - 3x^7 - x^5 + 3x^4 - 2x^3 - x^2 - x + 1	$10$	[2,4]	$3^{3}\cdot 1123^{3}$	$$	$11.4353721644$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$20.6325121629$
10.2.54470700288.2	x^10 - 2x^6 - 4x^3 + 4x^2 - 4x + 4	$10$	[2,4]	$2^{8}\cdot 3^{3}\cdot 199^{3}$	$$	$11.8472157061$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$33.313495222$
10.2.56409309184.1	x^10 - x^9 + 2x^8 - 7x^7 + 3x^6 + 2x^5 - 7x^4 + 5x^3 - 3x + 1	$10$	[2,4]	$2^{14}\cdot 151^{3}$	$$	$11.8887194342$				$S_5$ (as 10T13)	trivial	$2$	$5$	$45.5221642912$
10.2.57378463793.1	x^10 - x^9 + x^8 - 2x^7 + x^6 - 3x^5 + x^3 + x^2 + x + 1	$10$	[2,4]	$7^{3}\cdot 19^{3}\cdot 29^{3}$	$$	$11.9089889327$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$24.9742948243$
10.2.58818484369.1	x^10 - x^9 - x^8 + 2x^7 - 3x^6 - x^5 + 2x^4 - x^3 + 1	$10$	[2,4]	$3889^{3}$	$$	$11.9385445106$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$19.5377117302$
10.2.58968677632.1	x^10 - 2x^9 + 2x^8 - 2x^7 + 4x^5 - 8x^4 + 4x^3 + 4x^2 - 8x + 4	$10$	[2,4]	$2^{8}\cdot 613^{3}$	$$	$11.9415895259$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$27.5601543374$
10.2.59501707264.1	x^10 - 4x^9 + 5x^8 - 6x^6 + 4x^5 + 5x^2 - 1	$10$	[2,4]	$2^{18}\cdot 61^{3}$	$$	$11.9523401094$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$61.2859856522$
10.2.59897527569.1	x^10 - x^9 - x^8 - x^7 + 6x^6 + 5x^5 - 3x^4 - 4x^3 + x^2 + 5x - 1	$10$	[2,4]	$3^{8}\cdot 11^{3}\cdot 19^{3}$	$$	$11.9602674047$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$26.7498676466$
10.2.66331758592.2	x^10 - x^9 - 2x^8 + x^7 - 5x^6 - 2x^5 + 5x^4 - 3x^3 + x + 1	$10$	[2,4]	$2^{12}\cdot 11^{3}\cdot 23^{3}$	$$	$12.0829269856$				$S_5$ (as 10T13)	trivial	$2$	$5$	$36.4949128117$
10.2.72459558809.1	x^10 - 2x^9 - 2x^8 + 7x^7 - 3x^6 - 6x^5 + 4x^4 - 2x^3 + 4x^2 - x + 1	$10$	[2,4]	$11^{3}\cdot 379^{3}$	$$	$12.1901645645$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$25.8765661644$
10.4.72758649087.1	x^10 - x^9 + 3x^8 - 6x^7 - 3x^6 - 3x^5 - 6x^4 + 3x^3 + 2x + 1	$10$	[4,3]	$-\,3^{8}\cdot 223^{3}$	$$	$12.1951869594$			not computed	$S_5$ (as 10T13)	trivial	$2$	$6$	$30.6901611785$
10.4.74515853627.1	x^10 - 2x^9 + 2x^8 - x^7 - 5x^6 + 3x^5 - 3x^4 + x^3 + 7x^2 + 4x + 1	$10$	[4,3]	$-\,19^{4}\cdot 83^{3}$	$$	$12.2243244486$			not computed	$S_5$ (as 10T13)	trivial	$2$	$6$	$55.1347630923$
10.2.75049519552.1	x^10 - x^9 - 2x^8 - 3x^7 - 2x^6 + 4x^4 + x^3 + 3x^2 - 2x - 1	$10$	[2,4]	$2^{6}\cdot 7^{3}\cdot 43^{4}$	$$	$12.2330511495$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$46.5119692301$
10.2.77363231581.1	x^10 + 2x^8 - 4x^7 - 2x^6 - 2x^5 + 4x^4 - 2x^3 - 2x + 1	$10$	[2,4]	$4261^{3}$	$$	$12.2702513821$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$30.0397475333$
10.2.79433915648.1	x^10 + x^8 - 4x^7 + 4x^6 - 2x^5 - 6x^4 + 4x^3 - x^2 - 2x + 1	$10$	[2,4]	$2^{8}\cdot 677^{3}$	$$	$12.3027046238$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$34.3199517734$
10.2.85707789929.1	x^10 - 2x^8 - x^7 - 2x^6 + x^5 + 3x^4 - 2x^3 - x^2 + x + 1	$10$	[2,4]	$4409^{3}$	$$	$12.3965840598$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$24.4605225553$
10.2.86175179713.1	x^10 - 2x^9 + 2x^8 + x^7 - 3x^6 - 2x^5 - 2x^4 - 2x^2 - x + 1	$10$	[2,4]	$7^{3}\cdot 631^{3}$	$$	$12.4033277492$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$27.5240171192$
10.2.86879445589.1	x^10 - 2x^9 + x^8 - 2x^7 + 4x^6 - 5x^5 + x^4 - 2x^3 + x^2 + x + 1	$10$	[2,4]	$43^{3}\cdot 103^{3}$	$$	$12.4134272708$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$33.1655845358$
10.2.89734879333.1	x^10 - x^9 - x^8 + 2x^7 - x^6 - 3x^5 + 2x^4 + x^2 + 1	$10$	[2,4]	$11^{6}\cdot 37^{3}$	$$	$12.4536348668$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$35.9216147033$
10.4.91794884831.1	x^10 - x^9 + 4x^7 - 2x^6 - 2x^5 - x^4 + x^3 - 2x + 1	$10$	[4,3]	$-\,13^{3}\cdot 347^{3}$	$$	$12.4819330306$			not computed	$S_5$ (as 10T13)	trivial	$2$	$6$	$36.1853120565$
10.2.94134281149.2	x^10 - 2x^9 + 2x^8 - 3x^7 - 3x^6 + 4x^5 + x^4 - x^2 - 2x + 1	$10$	[2,4]	$4549^{3}$	$$	$12.51338426$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$44.7397967292$
10.2.97145684173.2	x^10 - x^9 + x^8 - 6x^7 + x^6 + x^5 + 6x^4 - 2x^3 - x^2 - 2x + 1	$10$	[2,4]	$4597^{3}$	$$	$12.5528503428$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$38.1005761988$
10.2.107365139712.2	x^10 - x^9 + x^8 + 4x^7 - 15x^6 + x^5 + 27x^4 - 14x^3 - 13x^2 + 11x - 1	$10$	[2,4]	$2^{8}\cdot 3^{4}\cdot 173^{3}$	$$	$12.6790387562$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$40.8746207381$
10.2.107646386093.1	x^10 - 2x^9 - x^8 + 6x^7 - 6x^6 - 3x^5 + 7x^4 - 4x^3 + 3x^2 - x + 1	$10$	[2,4]	$67^{3}\cdot 71^{3}$	$$	$12.6823561619$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$48.7653737163$
10.2.111771206513.1	x^10 - 2x^9 + x^7 - 3x^6 - 2x^5 + 8x^4 - 6x^3 + 2x^2 - x + 1	$10$	[2,4]	$4817^{3}$	$$	$12.7301345494$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$30.362674495$
10.2.117433042273.2	x^10 - x^9 - x^8 + 2x^7 - 3x^6 + 5x^5 - 2x^4 + 3x^3 + x^2 + x + 1	$10$	[2,4]	$59^{3}\cdot 83^{3}$	$$	$12.7931953401$			✓	$S_5$ (as 10T13)	trivial	$2$	$5$	$29.6416155266$
10.4.117865222327.1	x^10 - x^9 - x^8 + 3x^6 - 3x^5 - 8x^4 + 7x^3 - 2x + 1	$10$	[4,3]	$-\,4903^{3}$	$$	$12.7978957451$			not computed	$S_5$ (as 10T13)	trivial	$2$	$6$	$57.8296423144$
10.2.118940458033.1	x^10 - x^8 - 6x^7 - 3x^6 + x^5 - x^4 - 6x^3 - 8x^2 - 3x - 1	$10$	[2,4]	$19^{4}\cdot 97^{3}$	$$	$12.8095230837$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$35.0449643191$
10.4.126237434624.1	x^10 - 3x^9 + x^8 + 2x^7 - x^6 - 3x^5 + 11x^4 - 4x^3 + x^2 + 3x - 1	$10$	[4,3]	$-\,2^{8}\cdot 7^{4}\cdot 59^{3}$	$$	$12.886020444$			not computed	$S_5$ (as 10T13)	trivial	$2$	$6$	$55.7962913178$
10.2.126884390625.1	x^10 - 3x^7 - 2x^6 - 3x^5 + 3x^4 + 4x^3 + x^2 + x + 1	$10$	[2,4]	$3^{3}\cdot 5^{6}\cdot 67^{3}$	$$	$12.8926092378$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$53.1753805254$
10.2.129602962688.1	x^10 - 2x^9 - 2x^7 + 8x^6 - 4x^5 - 8x^3 + 4x^2 + 4	$10$	[2,4]	$2^{8}\cdot 797^{3}$	$$	$12.9199696346$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$51.4432096337$
10.2.132031254528.2	x^10 - 2x^9 + 2x^8 - 2x^7 + 3x^6 - 8x^5 + 9x^4 + 4x^3 - 20x^2 + 16x - 4	$10$	[2,4]	$2^{12}\cdot 3^{8}\cdot 17^{3}$	$$	$12.9439752835$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$64.7115102512$
10.4.133541229312.1	x^10 - 2x^9 - x^8 + 10x^7 - 6x^6 - 2x^5 + 6x^4 - 14x^3 + x^2 + 4x - 1	$10$	[4,3]	$-\,2^{8}\cdot 3^{8}\cdot 43^{3}$	$$	$12.9587030173$			not computed	$S_5$ (as 10T13)	trivial	$2$	$6$	$59.4906287429$
10.2.137707850944.1	x^10 - x^9 - 2x^8 + 7x^7 - 8x^6 + 2x^5 + 8x^4 - 5x^3 - x^2 + 1	$10$	[2,4]	$2^{6}\cdot 1291^{3}$	$$	$12.9985787634$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$66.5085583303$
10.2.150288260544.1	x^10 - 3x^9 + 8x^8 - 6x^7 + x^6 + 9x^5 - 5x^4 + 3x^3 + 5x^2 - 3x - 2	$10$	[2,4]	$2^{6}\cdot 3^{8}\cdot 71^{3}$	$$	$13.1127114888$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$68.5106452112$
10.2.160722988453.1	x^10 - 2x^9 + 4x^8 - 2x^7 - 2x^6 - 2x^5 - 2x^4 + 4x^3 - 2x^2 - 2x + 1	$10$	[2,4]	$5437^{3}$	$$	$13.2010294494$			not computed	$S_5$ (as 10T13)	trivial	$2$	$5$	$44.5320791146$

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