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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.3.372153638957891448013587938820096.1	x^21 + 11x^19 - 8x^18 + 72x^17 - 48x^16 + 204x^15 + 249x^13 + 376x^12 + 18x^11 + 62x^10 - 473x^9 - 1008x^8 - 975x^7 + 192x^6 - 324x^5 + 936x^4 + 368x^3 - 576x^2 - 128x + 128	\( -\,2^{14}\cdot 3^{36}\cdot 73^{6} \)	21T151	Trivial (GRH)
21.5.1116460916873674344040763816460288.1	x^21 - 6x^19 - 4x^18 + 108x^15 + 216x^14 - 261x^13 - 1048x^12 - 1080x^11 - 480x^10 + 1378x^9 + 5832x^8 + 7533x^7 - 1566x^6 - 16092x^5 - 21528x^4 - 14992x^3 - 6048x^2 - 1344x - 128	\( 2^{14}\cdot 3^{37}\cdot 73^{6} \)	21T151	Trivial (GRH)
21.3.20906801248251181022960306970083328.1	x^21 - 27x^15 - 54x^14 - 117x^13 - 224x^12 + 513x^11 + 2334x^10 + 3224x^9 + 2160x^8 - 1467x^7 - 10110x^6 - 20412x^5 - 22680x^4 - 15120x^3 - 6048x^2 - 1344x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 17^{6}\cdot 131^{6} \)	21T151	Trivial (GRH)
21.7.20906801248251181022960306970083328.1	x^21 + 3x^19 - 4x^18 - 36x^17 - 84x^16 - 460x^15 - 504x^14 - 861x^13 - 1196x^12 - 108x^11 - 2400x^10 + 6543x^9 + 6354x^8 - 6891x^7 - 1444x^6 - 1908x^5 - 1128x^4 + 2128x^3 - 288x^2 + 576x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 17^{6}\cdot 131^{6} \)	21T151	Trivial (GRH)
21.5.20906801248251181022960306970083328.1	x^21 - 21x^19 - 18x^18 + 189x^17 + 324x^16 - 897x^15 - 2430x^14 + 2115x^13 + 9736x^12 - 783x^11 - 22062x^10 - 8161x^9 + 27108x^8 + 19989x^7 - 14274x^6 - 19872x^5 - 2160x^4 + 7760x^3 + 5184x^2 + 1344x + 128	\( 2^{14}\cdot 3^{21}\cdot 17^{6}\cdot 131^{6} \)	21T151	Trivial (GRH)
21.7.319938495118356927821328886866296832.1	x^21 - 3x^19 - 2x^18 - 18x^17 - 24x^16 - 62x^15 - 108x^14 + 252x^13 + 848x^12 + 1350x^11 + 2004x^10 + 2224x^9 + 1440x^8 - 1707x^7 - 10142x^6 - 20412x^5 - 22680x^4 - 15120x^3 - 6048x^2 - 1344x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 11^{12}\cdot 29^{6} \)	21T151	Trivial (GRH)
21.9.7998462377958923195533222171657420800.1	x^21 - 21x^19 - 14x^18 + 171x^17 + 228x^16 - 707x^15 - 1566x^14 + 1629x^13 + 6896x^12 + 81x^11 - 20322x^10 - 19128x^9 + 25776x^8 + 59865x^7 + 17162x^6 - 67500x^5 - 104184x^4 - 74576x^3 - 30240x^2 - 6720x - 640	\( 2^{14}\cdot 3^{21}\cdot 5^{2}\cdot 11^{12}\cdot 29^{6} \)	21T151	Trivial (GRH)
21.9.34851637680834718765274831719128907776.1	x^21 - 18x^19 - 2x^18 + 45x^17 + 174x^16 - 214x^15 - 1116x^14 + 9906x^13 - 15026x^12 - 34911x^11 + 106704x^10 - 73813x^9 - 33354x^8 + 29901x^7 + 53194x^6 - 62604x^5 + 14064x^4 + 5872x^3 - 1440x^2 - 576x + 128	\( 2^{14}\cdot 3^{21}\cdot 17^{6}\cdot 131^{6}\cdot 1667 \)	21T151	Trivial (GRH)
21.11.10343288728827978523071854146763992353792.1	x^21 - 21x^19 - x^18 + 189x^17 + 18x^16 - 1101x^15 - 135x^14 + 5175x^13 + 1640x^12 - 19143x^11 - 14415x^10 + 45479x^9 + 60858x^8 - 49671x^7 - 122905x^6 - 9180x^5 + 109356x^4 + 53424x^3 - 30384x^2 - 19008x + 6208	\( -\,2^{10}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.13.165492619661247656369149666348223877660672.1	x^21 - 6x^19 - 4x^18 - 63x^17 - 84x^16 + 269x^15 + 594x^14 + 1692x^13 + 3544x^12 + 54x^11 - 9804x^10 - 22883x^9 - 42156x^8 - 52446x^7 - 27556x^6 + 17064x^5 + 39024x^4 + 29536x^3 + 12096x^2 + 2688x + 256	\( 2^{14}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.11.237714117824906601657941050896630528000000.1	x^21 - 3x^19 - 2x^18 - 90x^17 - 120x^16 + 68x^15 + 216x^14 + 1521x^13 + 3704x^12 + 2700x^11 - 1608x^10 - 9151x^9 - 23292x^8 - 32793x^7 - 20162x^6 + 5292x^5 + 18648x^4 + 14672x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 5^{6}\cdot 6679^{6} \)	21T151	Trivial (GRH)
21.15.237714117824906601657941050896630528000000.1	x^21 - 24x^19 - 16x^18 + 153x^17 + 204x^16 + 176x^15 + 216x^14 - 3420x^13 - 9472x^12 - 1485x^11 + 22506x^10 + 34207x^9 + 20844x^8 + 873x^7 - 13470x^6 - 22572x^5 - 23256x^4 - 15184x^3 - 6048x^2 - 1344x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 5^{6}\cdot 6679^{6} \)	21T151	Trivial (GRH)
21.15.330985239322495312738299332696447755321344.1	x^21 - 27x^19 - 18x^18 + 234x^17 + 312x^16 - 409x^15 - 1026x^14 - 2547x^13 - 5120x^12 + 621x^11 + 16422x^10 + 28117x^9 + 31140x^8 + 25446x^7 + 1924x^6 - 30024x^5 - 42480x^4 - 29920x^3 - 12096x^2 - 2688x - 256	\( -\,2^{15}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.17.330985239322495312738299332696447755321344.1	x^21 - 48x^19 - 32x^18 + 909x^17 + 1212x^16 - 8209x^15 - 17226x^14 + 31284x^13 + 111496x^12 + 7614x^11 - 304092x^10 - 350139x^9 + 142452x^8 + 622908x^7 + 500928x^6 + 12528x^5 - 272448x^4 - 231872x^3 - 96768x^2 - 21504x - 2048	\( 2^{15}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.7.8026392053570511333903758817888858066542592.1	x^21 - 21x^19 - 5x^18 + 189x^17 + 90x^16 - 1177x^15 - 675x^14 + 6315x^13 + 1984x^12 - 25983x^11 + 2517x^10 + 76399x^9 - 31374x^8 - 174051x^7 + 139683x^6 + 290088x^5 - 453996x^4 - 67056x^3 + 594000x^2 - 499968x + 147136	\( -\,2^{13}\cdot 3^{21}\cdot 97\cdot 149^{6}\cdot 211^{6} \)	21T151	$[2]$ (GRH)
21.19.10467408193573914265348716396525160262037504.1	x^21 - 54x^19 - 107x^18 + 1125x^17 + 4500x^16 - 8107x^15 - 67779x^14 - 36492x^13 + 407759x^12 + 726822x^11 - 648882x^10 - 2751741x^9 - 1664640x^8 + 2055372x^7 + 3207811x^6 + 1305252x^5 - 75792x^4 - 149384x^3 - 17568x^2 + 1632x + 128	\( -\,2^{12}\cdot 3^{21}\cdot 11\cdot 23\cdot 149^{6}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.13.24120549315626845915803563870253630169042944.1	x^21 - 21x^19 - 3x^18 + 189x^17 + 54x^16 - 1021x^15 - 405x^14 + 3975x^13 + 2216x^12 - 11943x^11 - 10797x^10 + 23903x^9 + 36558x^8 - 17487x^7 - 64299x^6 - 27972x^5 + 34740x^4 + 45128x^3 + 20304x^2 + 3936x + 256	\( 2^{12}\cdot 3^{21}\cdot 11\cdot 53\cdot 149^{6}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.17.29714264728113325207242631362078816000000000.1	x^21 - 42x^19 - 28x^18 + 639x^17 + 852x^16 - 3955x^15 - 8478x^14 + 5445x^13 + 28336x^12 + 28863x^11 + 10722x^10 - 26563x^9 - 104220x^8 - 181755x^7 - 202326x^6 - 177660x^5 - 133560x^4 - 77840x^3 - 30240x^2 - 6720x - 640	\( 2^{14}\cdot 3^{21}\cdot 5^{9}\cdot 6679^{6} \)	21T151	Trivial (GRH)
21.7.109390621596084700860007929456175983133704192.1	x^21 - 54x^19 - 142x^18 + 1125x^17 + 5550x^16 - 6017x^15 - 77418x^14 - 70674x^13 + 434534x^12 + 848124x^11 - 983280x^10 - 3192759x^9 + 1467252x^8 + 8862276x^7 + 2890596x^6 - 11439792x^5 - 12529152x^4 - 3350624x^3 + 785664x^2 + 160896x - 49664	\( -\,2^{14}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6}\cdot 661 \)	21T151	Trivial (GRH)
21.21.6422603076433360296030329401308220468133019648.1	x^21 - 69x^19 - 46x^18 + 1962x^17 + 2616x^16 - 28801x^15 - 59346x^14 + 217125x^13 + 675712x^12 - 580797x^11 - 3913446x^10 - 2291627x^9 + 9375876x^8 + 17178468x^7 + 3193040x^6 - 22447152x^5 - 33151104x^4 - 23541056x^3 - 9531648x^2 - 2118144x - 201728	\( 2^{14}\cdot 3^{21}\cdot 149^{6}\cdot 197^{2}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.9.19170455031989592890704656049558768930560000000.1	x^21 + 42x^19 - 28x^18 + 639x^17 - 852x^16 + 4145x^15 - 7722x^14 + 7173x^13 - 6544x^12 - 54621x^11 + 197670x^10 - 367691x^9 + 583164x^8 - 457071x^7 - 687778x^6 + 2292084x^5 - 2800296x^4 + 1911344x^3 - 768096x^2 + 170688x - 16256	\( 2^{14}\cdot 3^{21}\cdot 5^{7}\cdot 127^{2}\cdot 6679^{6} \)	21T151	Trivial (GRH)
21.19.376684621470118839904470766759029380731469611008.1	x^21 - 66x^19 - 44x^18 + 1755x^17 + 2340x^16 - 23304x^15 - 48168x^14 + 149733x^13 + 477784x^12 - 261576x^11 - 2272800x^10 - 1756043x^9 + 3891348x^8 + 8255907x^7 + 3442422x^6 - 6481188x^5 - 11018952x^4 - 8015728x^3 - 3259872x^2 - 724416x - 68992	\( -\,2^{14}\cdot 3^{45}\cdot 7^{4}\cdot 11^{2}\cdot 547^{6} \)	21T151	Trivial (GRH)
21.9.262279532795191301858328944366856470224404480000000.1	x^21 + 105x^19 - 70x^18 + 4257x^17 - 5676x^16 + 83405x^15 - 163026x^14 + 789975x^13 - 1840928x^12 + 2652939x^11 - 3594666x^10 - 8784901x^9 + 48065508x^8 - 80541009x^7 + 61367970x^6 - 10638324x^5 - 19795032x^4 + 18743248x^3 - 7941024x^2 + 1764672x - 168064	\( 2^{21}\cdot 3^{21}\cdot 5^{7}\cdot 13^{2}\cdot 101^{2}\cdot 6679^{6} \)	21T151	Trivial (GRH)
21.21.3938561358012927168760351207095524681785277184000000.1	x^21 - 84x^19 - 56x^18 + 2907x^17 + 3876x^16 - 52357x^15 - 107298x^14 + 498141x^13 + 1503232x^12 - 1956987x^11 - 10911882x^10 - 4065803x^9 + 34784676x^8 + 56724123x^7 - 3587546x^6 - 106446852x^5 - 146475144x^4 - 102597616x^3 - 41434848x^2 - 9207744x - 876928	\( 2^{14}\cdot 3^{21}\cdot 5^{6}\cdot 13^{2}\cdot 17^{2}\cdot 31^{2}\cdot 353\cdot 6679^{6} \)	21T151	Trivial (GRH)