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 matches 1-50 of 284)

Label	Polynomial	Discriminant	Galois group	Class group
15.15.140998454960622300613.1	x^15 - 6x^14 - 3x^13 + 80x^12 - 96x^11 - 330x^10 + 715x^9 + 308x^8 - 1694x^7 + 715x^6 + 1287x^5 - 1217x^4 + 53x^3 + 263x^2 - 76x + 1	\( 11^{14}\cdot 13^{5} \)	$S_3 \times C_5$ (as 15T4)	Trivial (GRH)
15.15.539190459461999816537.1	x^15 - x^14 - 23x^13 + 2x^12 + 169x^11 + 66x^10 - 473x^9 - 264x^8 + 572x^7 + 341x^6 - 297x^5 - 157x^4 + 69x^3 + 25x^2 - 6x - 1	\( 11^{14}\cdot 17^{5} \)	$S_3 \times C_5$ (as 15T4)	Trivial (GRH)
15.15.585891880179643237473.1	x^15 - x^14 - 21x^13 + 10x^12 + 165x^11 - 14x^10 - 597x^9 - 103x^8 + 994x^7 + 271x^6 - 683x^5 - 92x^4 + 197x^3 - 24x^2 - 7x + 1	\( 3^{6}\cdot 7^{10}\cdot 13^{3}\cdot 109^{3} \)	$S_5 \times C_3$ (as 15T24)	Trivial (GRH)
15.15.756943935220796320321.1	x^15 - x^14 - 14x^13 + 13x^12 + 78x^11 - 66x^10 - 220x^9 + 165x^8 + 330x^7 - 210x^6 - 252x^5 + 126x^4 + 84x^3 - 28x^2 - 8x + 1	\( 31^{14} \)	$C_{15}$ (as 15T1)	Trivial (GRH)
15.15.886528337182930278529.1	x^15 - x^14 - 22x^13 + 17x^12 + 166x^11 - 102x^10 - 533x^9 + 270x^8 + 729x^7 - 352x^6 - 393x^5 + 173x^4 + 80x^3 - 27x^2 - 6x + 1	\( 7^{10}\cdot 11^{12} \)	$C_{15}$ (as 15T1)	Trivial (GRH)
15.15.1006329085257882652672.1	x^15 - 5x^14 - 9x^13 + 71x^12 + 3x^11 - 367x^10 + 187x^9 + 827x^8 - 660x^7 - 740x^6 + 816x^5 + 86x^4 - 327x^3 + 127x^2 - 19x + 1	\( 2^{12}\cdot 7^{11}\cdot 499^{3} \)	$S_5 \times C_3$ (as 15T24)	Trivial (GRH)
15.15.5876871993914273277409.1	x^15 - 6x^14 + x^13 + 56x^12 - 89x^11 - 122x^10 + 358x^9 - 53x^8 - 418x^7 + 271x^6 + 122x^5 - 158x^4 + 22x^3 + 22x^2 - 9x + 1	\( 11^{12}\cdot 109^{2}\cdot 397^{2} \)	15T36	Trivial (GRH)
15.15.8489248153826893370401.1	x^15 - 4x^14 - 9x^13 + 54x^12 - 7x^11 - 226x^10 + 218x^9 + 293x^8 - 500x^7 + 15x^6 + 314x^5 - 152x^4 - 28x^3 + 40x^2 - 11x + 1	\( 11^{12}\cdot 52009^{2} \)	15T36	Trivial (GRH)
15.15.10943023107606534329121.1	x^15 - 27x^13 - 4x^12 + 252x^11 + 60x^10 - 976x^9 - 288x^8 + 1473x^7 + 384x^6 - 765x^5 - 168x^4 + 150x^3 + 27x^2 - 9x - 1	\( 3^{20}\cdot 11^{12} \)	$C_{15}$ (as 15T1)	Trivial (GRH)
15.15.14867888428662380090281.1	x^15 - 6x^14 + 62x^12 - 98x^11 - 133x^10 + 397x^9 - 69x^8 - 456x^7 + 310x^6 + 122x^5 - 173x^4 + 29x^3 + 21x^2 - 9x + 1	\( 31^{2}\cdot 61^{2}\cdot 401^{6} \)	15T46	Trivial (GRH)
15.15.25927809472547742867577.1	x^15 - 7x^14 + 7x^13 + 52x^12 - 129x^11 - 37x^10 + 368x^9 - 220x^8 - 305x^7 + 339x^6 + 26x^5 - 142x^4 + 39x^3 + 14x^2 - 8x + 1	\( 61^{3}\cdot 397^{3}\cdot 42727^{2} \)	15T78	Trivial (GRH)
15.15.29766469523035740663169.1	x^15 - x^14 - 24x^13 + 41x^12 + 165x^11 - 405x^10 - 180x^9 + 963x^8 - 172x^7 - 909x^6 + 338x^5 + 359x^4 - 143x^3 - 47x^2 + 16x - 1	\( 19^{6}\cdot 293^{6} \)	$A_5$ (as 15T5)	Trivial
15.15.55089924796575212472793.1	x^15 - 3x^14 - 13x^13 + 48x^12 + 35x^11 - 247x^10 + 98x^9 + 452x^8 - 449x^7 - 183x^6 + 412x^5 - 130x^4 - 61x^3 + 50x^2 - 12x + 1	\( 61^{5}\cdot 397^{3}\cdot 1021^{2} \)	15T78	Trivial (GRH)
15.15.123374497805640685368241.1	x^15 - 5x^14 - 9x^13 + 68x^12 - 10x^11 - 274x^10 + 184x^9 + 429x^8 - 405x^7 - 242x^6 + 311x^5 + 17x^4 - 83x^3 + 13x^2 + 5x - 1	\( 592661^{4} \)	15T28	Trivial (GRH)
15.15.127667878299171450781696.1	x^15 - 25x^13 - 27x^12 + 183x^11 + 358x^10 - 255x^9 - 1041x^8 - 456x^7 + 700x^6 + 710x^5 + 78x^4 - 157x^3 - 80x^2 - 15x - 1	\( 2^{18}\cdot 887^{6} \)	$A_5$ (as 15T5)	Trivial (GRH)
15.15.262047125362808326177593.1	x^15 - 36x^13 - 27x^12 + 459x^11 + 540x^10 - 2560x^9 - 3357x^8 + 7287x^7 + 8848x^6 - 11637x^5 - 9867x^4 + 10811x^3 + 3105x^2 - 4623x + 989	\( 3^{15}\cdot 11^{13}\cdot 23^{2} \)	15T44	Trivial (GRH)
15.15.432659002790862279847129.1	x^15 - 2x^14 - 33x^13 + 46x^12 + 402x^11 - 362x^10 - 2214x^9 + 1335x^8 + 5700x^7 - 2740x^6 - 6581x^5 + 2926x^4 + 2758x^3 - 1103x^2 - 373x + 131	\( 11^{12}\cdot 13^{10} \)	$C_{15}$ (as 15T1)	Trivial (GRH)
15.15.538669224823562138423296.1	x^15 - x^14 - 27x^13 + 48x^12 + 193x^11 - 437x^10 - 463x^9 + 1422x^8 + 309x^7 - 2017x^6 + 137x^5 + 1354x^4 - 184x^3 - 420x^2 + 40x + 46	\( 2^{12}\cdot 71^{6}\cdot 179^{4} \)	15T28	Trivial (GRH)
15.15.555278804074785034747904.1	x^15 - 2x^14 - 28x^13 + 22x^12 + 204x^11 - 144x^10 - 578x^9 + 424x^8 + 672x^7 - 448x^6 - 374x^5 + 192x^4 + 96x^3 - 32x^2 - 8x + 2	\( 2^{14}\cdot 37^{5}\cdot 7877^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial (GRH)
15.15.792952227088888747277125.1	x^15 - 35x^13 - 18x^12 + 403x^11 + 337x^10 - 1759x^9 - 1406x^8 + 3449x^7 + 2048x^6 - 2850x^5 - 1077x^4 + 761x^3 + 123x^2 - 13x - 1	\( 5^{3}\cdot 229^{6}\cdot 353^{3} \)	$S_5 \times S_3$ (as 15T29)	Trivial (GRH)
15.15.859597094013128457246001.1	x^15 - 2x^14 - 32x^13 + 54x^12 + 347x^11 - 483x^10 - 1679x^9 + 1890x^8 + 3855x^7 - 3407x^6 - 4257x^5 + 2719x^4 + 2199x^3 - 896x^2 - 413x + 97	\( 7^{12}\cdot 199^{6} \)	$D_5\times C_3$ (as 15T3)	Trivial (GRH)
15.15.1174482731945113540672849.1	x^15 - x^14 - 27x^13 + 22x^12 + 230x^11 - 157x^10 - 760x^9 + 399x^8 + 1014x^7 - 476x^6 - 540x^5 + 238x^4 + 94x^3 - 33x^2 - 6x + 1	\( 7^{10}\cdot 401^{6} \)	$D_5\times C_3$ (as 15T3)	Trivial (GRH)
15.15.1730160900125000000000000.1	x^15 - 30x^13 + 360x^11 - 12x^10 - 2200x^9 + 240x^8 + 7200x^7 - 1680x^6 - 11980x^5 + 4800x^4 + 7800x^3 - 4800x^2 + 400x + 104	\( 2^{12}\cdot 5^{15}\cdot 7^{12} \)	$F_5\times C_3$ (as 15T8)	Trivial (GRH)
15.15.2059511496355375228200617.1	x^15 - 2x^14 - 31x^13 + 56x^12 + 340x^11 - 528x^10 - 1654x^9 + 2135x^8 + 3636x^7 - 3826x^6 - 3451x^5 + 2550x^4 + 1492x^3 - 478x^2 - 258x - 25	\( 11^{5}\cdot 19^{6}\cdot 43^{7} \)	$D_5\times S_3$ (as 15T7)	Trivial (GRH)
15.15.3429179358086139904000000.1	x^15 - 25x^13 - 2x^12 + 229x^11 + 40x^10 - 981x^9 - 228x^8 + 2103x^7 + 546x^6 - 2175x^5 - 568x^4 + 923x^3 + 198x^2 - 120x - 8	\( 2^{18}\cdot 5^{6}\cdot 307^{6} \)	$S_5$ (as 15T10)	Trivial (GRH)
15.15.3658983920858973184000000.1	x^15 - 3x^14 - 27x^13 + 85x^12 + 201x^11 - 751x^10 - 255x^9 + 2109x^8 - 473x^7 - 2181x^6 + 883x^5 + 715x^4 - 261x^3 - 69x^2 + 19x - 1	\( 2^{16}\cdot 5^{6}\cdot 17^{6}\cdot 23^{6} \)	$S_5$ (as 15T10)	Trivial (GRH)
15.15.9876832533361318095112441.1	x^15 - x^14 - 28x^13 + 23x^12 + 276x^11 - 182x^10 - 1193x^9 + 592x^8 + 2307x^7 - 956x^6 - 1721x^5 + 908x^4 + 316x^3 - 262x^2 + 42x - 1	\( 61^{14} \)	$C_{15}$ (as 15T1)	Trivial (GRH)
15.15.11527956194382420421735424.1	x^15 - 7x^14 - 17x^13 + 228x^12 - 217x^11 - 2256x^10 + 5392x^9 + 5898x^8 - 30661x^7 + 17242x^6 + 46052x^5 - 67465x^4 + 22925x^3 + 4610x^2 - 1755x - 169	\( 2^{10}\cdot 17^{9}\cdot 37^{7} \)	$F_5 \times S_3$ (as 15T11)	Trivial (GRH)
15.15.15088641971036407470703125.1	x^15 - 35x^13 + 455x^11 - 70x^10 - 2800x^9 + 1225x^8 + 8575x^7 - 6475x^6 - 11375x^5 + 12250x^4 + 3500x^3 - 6125x^2 + 875	\( 3^{6}\cdot 5^{15}\cdot 7^{14} \)	$F_5\times C_3$ (as 15T8)	Trivial (GRH)
15.15.15904924067541390944821201.1	x^15 - 4x^14 - 10x^13 + 58x^12 - 6x^11 - 249x^10 + 241x^9 + 323x^8 - 560x^7 + 28x^6 + 348x^5 - 181x^4 - 19x^3 + 39x^2 - 11x + 1	\( 127^{2}\cdot 401^{6}\cdot 487^{2} \)	15T46	Trivial (GRH)
15.15.16836836874485015869140625.1	x^15 - 5x^14 - 30x^13 + 150x^12 + 305x^11 - 1539x^10 - 1350x^9 + 6825x^8 + 3115x^7 - 13645x^6 - 4757x^5 + 11735x^4 + 3765x^3 - 3500x^2 - 770x + 301	\( 5^{24}\cdot 7^{10} \)	$C_{15}$ (as 15T1)	Trivial (GRH)
15.15.19241912323039288533050521.1	x^15 - 2x^14 - 43x^13 + 100x^12 + 622x^11 - 1668x^10 - 3380x^9 + 11013x^8 + 4836x^7 - 27366x^6 + 3839x^5 + 23300x^4 - 6520x^3 - 6663x^2 + 1723x + 197	\( 11^{12}\cdot 19^{10} \)	$C_{15}$ (as 15T1)	Trivial (GRH)
15.15.19616877526450987759846617.1	x^15 - 48x^13 - 32x^12 + 882x^11 + 1176x^10 - 7303x^9 - 15390x^8 + 21330x^7 + 81960x^6 + 35883x^5 - 123750x^4 - 208680x^3 - 143280x^2 - 47760x - 6368	\( 3^{15}\cdot 11^{13}\cdot 199^{2} \)	15T44	Trivial (GRH)
15.15.23775427618300208865265216.1	x^15 - 5x^14 - 28x^13 + 152x^12 + 176x^11 - 1487x^10 + 469x^9 + 5132x^8 - 5065x^7 - 4815x^6 + 7386x^5 + 349x^4 - 2933x^3 + 387x^2 + 267x + 13	\( 2^{6}\cdot 7^{10}\cdot 331^{6} \)	$\GL(2,4)$ (as 15T16)	Trivial (GRH)
15.15.23980112932460739050668032.1	x^15 - 24x^13 - 27x^12 + 167x^11 + 341x^10 - 181x^9 - 864x^8 - 357x^7 + 621x^6 + 583x^5 + 16x^4 - 170x^3 - 81x^2 - 15x - 1	\( 2^{16}\cdot 3^{4}\cdot 37^{2}\cdot 53^{9} \)	15T56	Trivial (GRH)
15.15.24616451192000000000000000.1	x^15 - 30x^13 + 360x^11 - 26x^10 - 2200x^9 + 520x^8 + 7200x^7 - 3640x^6 - 11790x^5 + 10400x^4 + 5900x^3 - 10400x^2 + 4200x - 496	\( 2^{18}\cdot 5^{15}\cdot 79^{5} \)	15T27	Trivial (GRH)
15.15.28424095136369691319629376.1	x^15 - 2x^14 - 41x^13 + 125x^12 + 437x^11 - 2057x^10 + 153x^9 + 10144x^8 - 16303x^7 + 721x^6 + 23221x^5 - 28390x^4 + 16191x^3 - 4896x^2 + 736x - 41	\( 2^{6}\cdot 7^{10}\cdot 11^{6}\cdot 31^{6} \)	$\GL(2,4)$ (as 15T16)	Trivial (GRH)
15.15.49790403910409826929475584.1	x^15 - 3x^14 - 36x^13 + 166x^12 + 118x^11 - 1666x^10 + 2156x^9 + 2800x^8 - 7863x^7 + 2941x^6 + 4612x^5 - 3330x^4 - 348x^3 + 428x^2 + 16x - 8	\( 2^{18}\cdot 11^{6}\cdot 101^{7} \)	$D_5\times S_3$ (as 15T7)	Trivial (GRH)
15.15.63095343954661026090442701.1	x^15 - 3x^14 - 33x^13 + 80x^12 + 411x^11 - 813x^10 - 2371x^9 + 4050x^8 + 6279x^7 - 10380x^6 - 6255x^5 + 12105x^4 - 144x^3 - 4041x^2 + 1350x - 123	\( 3^{21}\cdot 11^{6}\cdot 23^{7} \)	$A_5 \times S_3$ (as 15T23)	Trivial (GRH)
15.15.138622929316925604547946697.1	x^15 - 75x^13 - 123x^12 + 1854x^11 + 5532x^10 - 15374x^9 - 79524x^8 - 19527x^7 + 386911x^6 + 652257x^5 - 170775x^4 - 1591761x^3 - 1909161x^2 - 991875x - 197317	\( 3^{15}\cdot 11^{13}\cdot 23^{4} \)	15T33	Trivial (GRH)
15.15.138622929316925604547946697.2	x^15 - 60x^13 - 63x^12 + 1341x^11 + 2727x^10 - 12674x^9 - 40869x^8 + 31254x^7 + 243271x^6 + 196857x^5 - 393162x^4 - 847458x^3 - 566559x^2 - 111090x + 12167	\( 3^{15}\cdot 11^{13}\cdot 23^{4} \)	15T33	Trivial (GRH)
15.15.207828545629978179931640625.1	x^15 - 45x^13 - 10x^12 + 690x^11 + 252x^10 - 4560x^9 - 1965x^8 + 14370x^7 + 6350x^6 - 21975x^5 - 8970x^4 + 15050x^3 + 4575x^2 - 3405x - 107	\( 3^{20}\cdot 5^{24} \)	$C_{15}$ (as 15T1)	Trivial (GRH)
15.15.222495240978703757087365489.1	x^15 - 2x^14 - 47x^13 + 44x^12 + 796x^11 - 86x^10 - 5782x^9 - 2469x^8 + 18376x^7 + 14370x^6 - 21477x^5 - 22698x^4 + 4468x^3 + 10091x^2 + 2903x + 211	\( 7^{10}\cdot 31^{12} \)	$C_{15}$ (as 15T1)	Trivial (GRH)
15.15.346719785000000000000000000.1	x^15 - 35x^13 + 440x^11 - 78x^10 - 2525x^9 + 1190x^8 + 6850x^7 - 5260x^6 - 7469x^5 + 7750x^4 + 1725x^3 - 2750x^2 - 100x + 260	\( 2^{18}\cdot 5^{19}\cdot 37^{5} \)	15T49	Trivial (GRH)
15.15.401095849317140421258328161.1	x^15 - 48x^13 - 4x^12 + 720x^11 - 111x^10 - 4259x^9 + 1809x^8 + 10989x^7 - 7125x^6 - 11826x^5 + 10260x^4 + 3483x^3 - 4617x^2 + 486x + 243	\( 3^{19}\cdot 83\cdot 401^{6} \)	15T86	Trivial (GRH)
15.15.428215667734040018945816133.1	x^15 - 39x^13 - 34x^12 + 531x^11 + 789x^10 - 2982x^9 - 5922x^8 + 6669x^7 + 18631x^6 - 2295x^5 - 23463x^4 - 7569x^3 + 7290x^2 + 2151x - 831	\( 3^{23}\cdot 19^{3}\cdot 37\cdot 2617^{3} \)	15T93	Trivial (GRH)
15.15.430807787028125000000000000.1	x^15 - 35x^13 + 425x^11 - 76x^10 - 2350x^9 + 820x^8 + 6225x^7 - 2580x^6 - 7880x^5 + 2750x^4 + 4525x^3 - 500x^2 - 1100x - 200	\( 2^{12}\cdot 5^{17}\cdot 13^{10} \)	15T38	Trivial (GRH)
15.15.725031474691613510491573833.1	x^15 - 48x^13 - 18x^12 + 837x^11 + 525x^10 - 6713x^9 - 5481x^8 + 25770x^7 + 24378x^6 - 45144x^5 - 45111x^4 + 35431x^3 + 35937x^2 - 10164x - 10285	\( 3^{20}\cdot 11^{4}\cdot 61^{3}\cdot 397^{3} \)	15T63	Trivial (GRH)
15.15.897397249918108651776000000.1	x^15 - 3x^14 - 37x^13 + 91x^12 + 483x^11 - 829x^10 - 2993x^9 + 2941x^8 + 9853x^7 - 3339x^6 - 16675x^5 - 2811x^4 + 11401x^3 + 6327x^2 - 59x - 401	\( 2^{14}\cdot 3^{6}\cdot 5^{6}\cdot 37^{10} \)	$C_{15} : C_4$ (as 15T6)	Trivial (GRH)
15.15.1008471948336125000000000000.1	x^15 - 40x^13 + 605x^11 - 92x^10 - 4450x^9 + 1870x^8 + 16825x^7 - 12460x^6 - 29575x^5 + 32500x^4 + 14105x^3 - 26650x^2 + 5980x + 1352	\( 2^{12}\cdot 5^{15}\cdot 7^{10}\cdot 13^{4} \)	15T38	Trivial (GRH)