Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 11 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.1.18494950052095344498131861504.1	x^15 - x^14 - 4x^13 - 54x^12 + 77x^11 + 319x^10 + 1407x^9 - 9201x^8 + 12239x^7 - 12671x^6 + 86954x^5 - 263536x^4 + 424387x^3 - 426463x^2 + 359739x - 107657	\( -\,2^{23}\cdot 13^{5}\cdot 53^{2}\cdot 1453943^{2} \)	15T96	$[3]$ (GRH)
15.1.26826201586624000000000000000000.1	x^15 - 75x^11 - 24x^10 + 2050x^7 + 480x^6 + 720x^5 - 15125x^3 - 12100x^2 - 7744	\( -\,2^{24}\cdot 5^{18}\cdot 11^{4}\cdot 31^{5} \)	15T96	$[3]$ (GRH)
15.3.1744064843158258782713344097088061.1	x^15 - 4x^14 - 6x^13 + 24x^12 + 1117x^11 + 780x^10 + 2624x^9 - 648x^8 + 254304x^7 + 164960x^6 + 618496x^5 + 70400x^4 + 16000768x^3 + 2560000x^2 - 512000x - 16384	\( 229^{5}\cdot 120721^{2}\cdot 435923^{2} \)	15T96	$[3]$ (GRH)
15.3.3138922448058688000000000000000000.1	x^15 + 160x^11 - 128x^10 + 5200x^7 - 8320x^6 + 3328x^5 - 14500x^3 + 34800x^2 - 27840x + 7424	\( 2^{24}\cdot 5^{18}\cdot 29^{4}\cdot 37^{5} \)	15T96	$[3]$ (GRH)
15.11.22639092611819562236124731312177152000000.1	x^15 - 234x^13 - 936x^12 + 10592x^11 + 91756x^10 + 318690x^9 + 925776x^8 + 2973004x^7 + 7361212x^6 + 11707090x^5 + 11784960x^4 + 7512850x^3 + 2948100x^2 + 651000x + 62000	\( 2^{24}\cdot 5^{6}\cdot 23^{2}\cdot 31^{4}\cdot 37^{5}\cdot 1596629^{2} \)	15T96	$[3]$ (GRH)
15.7.87173191285397298520836997842731008000000.1	x^15 - 144x^13 - 1008x^12 + 754x^11 + 37432x^10 + 182394x^9 + 94320x^8 - 1412708x^7 - 1669256x^6 + 4312160x^5 + 6973920x^4 - 1537000x^3 - 6681600x^2 - 3248000x - 464000	\( 2^{24}\cdot 5^{6}\cdot 13^{2}\cdot 29^{4}\cdot 37^{5}\cdot 151^{2}\cdot 41947^{2} \)	15T96	$[3]$ (GRH)
15.7.637858372296192230986633844231104626688000000.1	x^15 - 126x^13 - 72x^12 + 770x^11 + 74696x^10 - 252486x^9 - 2674152x^8 + 17570644x^7 - 30046744x^6 - 13423800x^5 + 75319920x^4 - 40593800x^3 - 17576000x^2 + 9464000x + 2704000	\( 2^{24}\cdot 5^{6}\cdot 13^{8}\cdot 37^{5}\cdot 67^{2}\cdot 3095563^{2} \)	15T96	$[3]$ (GRH)
15.11.1584541601971758745306546692340589068288000000.1	x^15 - 684x^13 - 432x^12 + 146384x^11 + 86128x^10 - 12084336x^9 - 4014720x^8 + 382478112x^7 - 471272384x^6 - 1146538240x^5 + 1889210880x^4 + 416368000x^3 - 1810022400x^2 + 879872000x - 125696000	\( 2^{22}\cdot 5^{6}\cdot 19^{2}\cdot 37^{5}\cdot 491^{4}\cdot 1307^{2}\cdot 3119^{2} \)	15T96	$[3]$ (GRH)
15.5.12170194953371312791319056980973540985335808000000.1	x^15 - 792x^13 - 288x^12 + 196268x^11 + 645184x^10 - 16875000x^9 - 113494464x^8 - 230315360x^7 + 2578282496x^6 + 7254954240x^5 + 4806282240x^4 - 11221875200x^3 - 14577612800x^2 + 11546624000	\( -\,2^{18}\cdot 5^{6}\cdot 7^{4}\cdot 23^{7}\cdot 2819^{4}\cdot 2399027^{2} \)	15T96	$[3]$ (GRH)
15.15.3550599197078961086196327997289859114171513438208000000.1	x^15 - 1386x^13 - 11448x^12 + 529090x^11 + 8049544x^10 - 14432166x^9 - 801109368x^8 - 4342753996x^7 - 7195456296x^6 + 3079532200x^5 + 17546867280x^4 + 9456914200x^3 - 4094584000x^2 - 2204776000x + 629936000	\( 2^{24}\cdot 5^{6}\cdot 23^{2}\cdot 37^{5}\cdot 67^{2}\cdot 39371^{4}\cdot 185021^{2} \)	15T96	$[3]$ (GRH)
15.15.263067183205872529212832748534985625689305855623168000000.1	x^15 - 2754x^13 - 11016x^12 + 1610262x^11 + 12964716x^10 - 84517920x^9 - 1422699984x^8 - 7303718236x^7 - 19757797408x^6 - 31834343560x^5 - 32087024640x^4 - 20455309400x^3 - 8026820400x^2 - 1772484000x - 168808000	\( 2^{22}\cdot 5^{6}\cdot 23^{2}\cdot 37^{5}\cdot 491^{2}\cdot 21101^{4}\cdot 1513121^{2} \)	15T96	$[3]$ (GRH)