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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.8.732780301186512843008.2	x^16 - 4x^15 - x^14 + 21x^13 - 16x^12 - 21x^11 - 35x^10 + 106x^9 + 171x^8 - 497x^7 + 135x^6 + 378x^5 - 118x^4 - 259x^3 + 169x^2 - 30x + 1	\( 2^{8}\cdot 17^{15} \)	16T841	Trivial
16.8.12849417078227563094777.3	x^16 - x^15 + x^14 - 18x^13 + x^12 - x^11 + 69x^10 + 101x^9 + x^8 - 35x^7 - 169x^6 - 358x^5 - 237x^4 - x^3 + 52x^2 + 16x + 1	\( 17^{15}\cdot 67^{2} \)	16T841	Trivial (GRH)
16.12.187591757103747287810048.3	x^16 - 34x^12 + 34x^10 + 221x^8 - 544x^6 + 459x^4 - 153x^2 + 17	\( 2^{16}\cdot 17^{15} \)	16T841	Trivial (GRH)
16.4.187591757103747287810048.3	x^16 - 34x^12 - 34x^10 + 221x^8 + 544x^6 + 459x^4 + 153x^2 + 17	\( 2^{16}\cdot 17^{15} \)	16T841	$[2]$ (GRH)
16.8.187591757103747287810048.6	x^16 - 34x^12 + 51x^10 + 170x^8 - 306x^6 - 34x^4 + 119x^2 + 17	\( 2^{16}\cdot 17^{15} \)	16T841	Trivial (GRH)
16.12.604462909807314587353088.1	x^16 - 16x^14 + 96x^12 - 256x^10 + 232x^8 + 192x^6 - 416x^4 + 128x^2 + 8	\( 2^{79} \)	16T841	Trivial (GRH)
16.8.604462909807314587353088.4	x^16 - 24x^12 + 16x^10 + 132x^8 - 64x^6 - 192x^4 - 64x^2 + 2	\( 2^{79} \)	16T841	Trivial (GRH)
16.8.604462909807314587353088.5	x^16 - 24x^12 - 16x^10 + 132x^8 + 64x^6 - 192x^4 + 64x^2 + 2	\( 2^{79} \)	16T841	Trivial (GRH)
16.4.604462909807314587353088.9	x^16 + 16x^14 + 96x^12 + 256x^10 + 232x^8 - 192x^6 - 416x^4 - 128x^2 + 8	\( 2^{79} \)	16T841	Trivial (GRH)
16.16.3289450772026256152262912.1	x^16 - 6x^15 - 15x^14 + 141x^13 + 4x^12 - 1248x^11 + 1045x^10 + 5035x^9 - 6954x^8 - 8307x^7 + 17627x^6 + 641x^5 - 16579x^4 + 8898x^3 + 1488x^2 - 2213x + 443	\( 2^{8}\cdot 17^{15}\cdot 67^{2} \)	16T841	Trivial (GRH)
16.4.7774066215287714751471872.1	x^16 - 5x^15 + 25x^14 - 40x^13 + 64x^12 + 207x^11 - 491x^10 + 1639x^9 - 1616x^8 + 1535x^7 - 1963x^6 - 2646x^5 - 10621x^4 - 4627x^3 - 17852x^2 - 9918x - 1291	\( 2^{8}\cdot 17^{15}\cdot 103^{2} \)	16T841	$[2]$ (GRH)
16.4.7774066215287714751471872.2	x^16 - 5x^15 + 25x^14 - 57x^13 + 132x^12 - 269x^11 + 614x^10 - 1268x^9 + 2158x^8 - 2392x^7 + 3171x^6 - 3564x^5 + 3268x^4 - 8605x^3 - 12242x^2 + 13797x + 8093	\( 2^{8}\cdot 17^{15}\cdot 103^{2} \)	16T841	$[2]$ (GRH)
16.12.57681033264163530732453953.3	x^16 - 7x^15 + 15x^14 - 20x^13 - 13x^12 + 414x^11 - 1062x^10 + 1093x^9 + 339x^8 - 8748x^7 + 8417x^6 + 17904x^5 - 11054x^4 - 15255x^3 + 1997x^2 + 4551x + 919	\( 17^{15}\cdot 67^{4} \)	16T841	Trivial (GRH)
16.4.57681033264163530732453953.4	x^16 - 2x^15 + 4x^14 + 26x^13 - 69x^12 + 138x^11 - 208x^10 - 60x^9 + x^8 - 3606x^7 + 684x^6 - 127x^5 + 11899x^4 - 2310x^3 + 32891x^2 - 16142x + 31247	\( 17^{15}\cdot 67^{4} \)	16T841	$[2, 2]$ (GRH)
16.8.842099397638721574979305472.1	x^16 + 17x^14 - 34x^12 - 1122x^10 + 629x^8 + 20910x^6 - 10438x^4 - 108205x^2 + 76313	\( 2^{16}\cdot 17^{15}\cdot 67^{2} \)	16T841	$[2]$ (GRH)
16.8.842099397638721574979305472.2	x^16 - 272x^12 + 408x^10 + 15657x^8 - 14382x^6 - 73117x^4 + 42143x^2 + 76313	\( 2^{16}\cdot 17^{15}\cdot 67^{2} \)	16T841	$[2]$ (GRH)
16.0.842099397638721574979305472.3	x^16 + 51x^14 + 969x^12 + 9452x^10 + 52751x^8 + 172652x^6 + 318002x^4 + 284750x^2 + 76313	\( 2^{16}\cdot 17^{15}\cdot 67^{2} \)	16T841	$[2, 2, 2, 148]$ (GRH)
16.12.1990160951113654976376799232.3	x^16 - 17x^14 - 68x^12 + 2414x^10 - 11203x^8 - 6630x^6 + 145180x^4 - 299421x^2 + 180353	\( 2^{16}\cdot 17^{15}\cdot 103^{2} \)	16T841	Trivial (GRH)
16.12.1990160951113654976376799232.4	x^16 - 17x^14 - 102x^12 + 2074x^10 - 4029x^8 - 38794x^6 + 194514x^4 - 320433x^2 + 180353	\( 2^{16}\cdot 17^{15}\cdot 103^{2} \)	16T841	Trivial (GRH)
16.0.2128929593223415400006494769.1	x^16 - 6x^15 + 22x^14 - 18x^13 - 119x^12 + 431x^11 - 673x^10 + 567x^9 + 1117x^8 - 6372x^7 + 15258x^6 - 22650x^5 + 21474x^4 - 6357x^3 - 4247x^2 + 1838x + 857	\( 37^{2}\cdot 41^{15} \)	16T841	Trivial (GRH)
16.0.5687391518377022952405204992.3	x^16 + 16x^14 + 72x^12 + 64x^10 + 1476x^8 + 12704x^6 + 24048x^4 + 18818	\( 2^{79}\cdot 97^{2} \)	16T841	Trivial (GRH)
16.0.5687391518377022952405204992.4	x^16 + 16x^14 + 216x^12 + 1696x^10 + 8020x^8 + 23712x^6 + 42928x^4 + 43456x^2 + 18818	\( 2^{79}\cdot 97^{2} \)	16T841	Trivial (GRH)
16.0.31236842166910780816202985728.1	x^16 - 5x^15 + 93x^14 - 448x^13 + 3940x^12 - 16657x^11 + 93145x^10 - 335097x^9 + 1301332x^8 - 3803949x^7 + 10438655x^6 - 23104150x^5 + 43654491x^4 - 65201089x^3 + 76529340x^2 - 57494058x + 24212557	\( 2^{8}\cdot 17^{15}\cdot 6529^{2} \)	16T841	$[2, 4, 984]$ (GRH)
16.16.31236842166910780816202985728.1	x^16 - 5x^15 - 77x^14 + 368x^13 + 2206x^12 - 10163x^11 - 29408x^10 + 130754x^9 + 189583x^8 - 798655x^7 - 601077x^6 + 2153889x^5 + 1216201x^4 - 2470290x^3 - 1359220x^2 + 997927x + 589493	\( 2^{8}\cdot 17^{15}\cdot 6529^{2} \)	16T841	Trivial (GRH)
16.8.258930158322830089457985795017.7	x^16 - 4x^15 + 16x^14 - 98x^13 - 169x^12 + 115x^11 + 577x^10 + 17140x^9 - 16387x^8 + 146145x^7 - 267734x^6 - 971393x^5 + 4095607x^4 - 16651844x^3 - 15288526x^2 + 70702018x + 11279467	\( 17^{15}\cdot 67^{6} \)	16T841	$[2, 2]$ (GRH)
16.8.292906977896507671746287067392.1	x^16 - 3x^15 + 9x^14 - 95x^13 - 361x^12 + 1253x^11 - 648x^10 + 17482x^9 + 26519x^8 - 35578x^7 + 310904x^6 - 223744x^5 - 3002672x^4 - 16048352x^3 - 37194264x^2 - 8998752x + 21705584	\( 2^{8}\cdot 17^{15}\cdot 19993^{2} \)	16T841	Trivial (GRH)
16.0.2914504613122855682608891338761.2	x^16 - 4x^15 + 28x^14 - 19x^13 + 59x^12 + 842x^11 + 7x^10 - 1417x^9 + 6045x^8 + 12419x^7 - 14665x^6 - 74851x^5 - 49199x^4 + 121382x^3 + 231785x^2 + 142491x + 50153	\( 37^{4}\cdot 41^{15} \)	16T841	$[2]$ (GRH)
16.0.2914504613122855682608891338761.3	x^16 - 3x^15 - 15x^14 + 49x^13 - 92x^12 + 476x^11 + 1379x^10 - 9661x^9 + 24109x^8 + 1428x^7 - 67861x^6 + 59049x^5 + 407030x^4 - 1268099x^3 + 1779996x^2 - 1223664x + 387427	\( 37^{4}\cdot 41^{15} \)	16T841	$[2]$ (GRH)
16.0.12196812568090154832283098089233.1	x^16 - 8x^15 + 30x^14 - 70x^13 + 132x^12 - 246x^11 - 4264x^10 + 22860x^9 + 17710x^8 - 209562x^7 + 71748x^6 + 615758x^5 - 590233x^4 - 136764x^3 + 1053996x^2 - 841088x + 375808	\( 37^{2}\cdot 73^{15} \)	16T841	$[89]$ (GRH)
16.8.2356327674777993305467029827040553.2	x^16 - 8x^15 + 30x^14 - 70x^13 - 1026x^12 + 6702x^11 - 15504x^10 + 15370x^9 + 280960x^8 - 1141194x^7 + 1930786x^6 - 1808530x^5 - 13917442x^4 + 29524424x^3 - 20810458x^2 + 5935959x - 493501	\( 61^{2}\cdot 97^{15} \)	16T841	$[2]$ (GRH)
16.0.3989956815365189429491572242763809.1	x^16 - 3x^15 - 15x^14 + 49x^13 - 256x^12 + 1132x^11 + 4741x^10 - 24954x^9 + 22141x^8 - 347359x^7 + 2771348x^6 - 9301087x^5 + 19361822x^4 - 31135328x^3 + 38788769x^2 - 27400483x + 8278943	\( 37^{6}\cdot 41^{15} \)	16T841	$[2, 2, 2]$ (GRH)
16.0.16697436405715421965395561284159977.1	x^16 - 5x^15 + 14x^14 - 136x^13 + 786x^12 - 2378x^11 + 18306x^10 - 55432x^9 + 66258x^8 - 415744x^7 + 1686286x^6 - 2215390x^5 + 2146605x^4 - 12386043x^3 + 36407032x^2 - 43706312x + 19765336	\( 37^{4}\cdot 73^{15} \)	16T841	$[178]$ (GRH)
16.0.16697436405715421965395561284159977.3	x^16 - 7x^15 + 7x^14 + 80x^13 + 233x^12 - 1993x^11 - 8753x^10 + 59080x^9 + 301680x^8 - 3576936x^7 + 14199152x^6 - 28593728x^5 + 25364608x^4 + 4748416x^3 - 4564992x^2 - 67074048x + 102711296	\( 37^{4}\cdot 73^{15} \)	16T841	$[178]$ (GRH)
16.8.519500614265953437911136445884676352.1	x^16 - 4x^15 + 305x^14 - 591x^13 - 2277x^12 - 29499x^11 - 4287707x^10 - 9682635x^9 - 22008114x^8 + 448957127x^7 + 13256524043x^6 + 28506195667x^5 - 91601657871x^4 - 672880822233x^3 - 5109366359220x^2 - 1215733652348x + 43106377080817	\( 2^{8}\cdot 17^{15}\cdot 26626013^{2} \)	16T841	Trivial (GRH)
16.8.8767895277848913089642817986417897713.2	x^16 - 5x^15 + 39x^14 + 125x^13 - 8134x^12 + 8768x^11 + 25855x^10 - 314877x^9 + 1291073x^8 - 3231766x^7 - 5743921x^6 + 36806443x^5 - 51369568x^4 + 15105765x^3 + 16830832x^2 - 8408452x - 939737	\( 61^{4}\cdot 97^{15} \)	16T841	$[4]$ (GRH)
16.8.8767895277848913089642817986417897713.7	x^16 - 6x^15 - 68x^14 + 216x^13 + 1992x^12 + 5230x^11 - 80068x^10 + 163132x^9 + 1105782x^8 - 10260945x^7 - 28171423x^6 + 192753639x^5 + 977105421x^4 - 4184728814x^3 - 15831634490x^2 + 57264732095x + 167363472977	\( 61^{4}\cdot 97^{15} \)	16T841	$[2, 2]$ (GRH)
16.0.22858790439424412670626523398015008513.5	x^16 - 4x^15 + 117x^14 - 611x^13 + 3421x^12 - 18171x^11 + 47429x^10 - 478033x^9 + 48414x^8 + 5391363x^7 + 97125874x^6 - 14629984x^5 + 477553112x^4 - 3203742192x^3 + 3724493056x^2 - 15384971776x + 28380726272	\( 37^{6}\cdot 73^{15} \)	16T841	$[2, 2, 178]$ (GRH)
16.8.29972682638651894650701256229375114805248.1	x^16 - 1020x^14 - 583899x^12 + 311883224x^10 + 87007049988x^8 - 18614015293632x^6 - 2580057810918438x^4 + 390453736425761706x^2 + 2716193998733560817	\( 2^{16}\cdot 17^{15}\cdot 19993^{4} \)	16T841	$[2, 2, 4]$ (GRH)
16.8.32625338328875805606560925727460997390073.3	x^16 - 4x^15 - 235x^14 + 1519x^13 + 8775x^12 - 108182x^11 + 345102x^10 + 2756222x^9 - 15226884x^8 - 116261286x^7 + 506360379x^6 + 1312007365x^5 - 7952268139x^4 - 15167591488x^3 + 75820476938x^2 + 243748531790x + 183952147391	\( 61^{6}\cdot 97^{15} \)	16T841	$[2, 4]$ (GRH)
16.8.94284067507195126346045323522879461199867166580604928.1	x^16 - 19890x^14 - 638585467x^12 + 1798329785850x^10 + 60897826532184704x^8 - 105732588674541402x^6 - 1577424202471246092688679x^4 - 1357399571910239703957606270x^2 + 8544240815100822030896306381537	\( 2^{16}\cdot 17^{15}\cdot 26626013^{4} \)	16T841	$[2, 2]$ (GRH)