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 60)

Label	Polynomial	Discriminant	Galois group	Class group
22.2.52963188445448362085110426970892.1	x^22 - 4x^21 + 8x^20 - 17x^19 + 25x^18 + 9x^17 - 75x^16 + 78x^15 - 51x^14 - 5x^13 + 143x^12 - 112x^11 + 22x^10 + 109x^9 + 123x^8 + 246x^7 + 108x^6 - 39x^5 - 82x^4 - 107x^3 - 65x^2 - 4x + 8	\( 2^{2}\cdot 3^{20}\cdot 11^{18}\cdot 683 \)	22T37	Trivial (GRH)
22.2.145648768224982995734053674169953.1	x^22 - 4x^21 + x^20 + 6x^19 + 21x^18 - 27x^17 - 24x^16 - 255x^15 + 291x^14 + 226x^13 + 1112x^12 + 1378x^11 + 1776x^10 + 2229x^9 + 2715x^8 + 2358x^7 + 1791x^6 + 360x^5 - 828x^4 - 9x^3 + 405x^2 + 117x - 72	\( 3^{20}\cdot 11^{19}\cdot 683 \)	22T37	Trivial (GRH)
22.0.158889565336345086255331280912676.1	x^22 - 11x^21 + 66x^20 - 275x^19 + 880x^18 - 2277x^17 + 4917x^16 - 9042x^15 + 14355x^14 - 19855x^13 + 24068x^12 - 25650x^11 + 24035x^10 - 19723x^9 + 14058x^8 - 8646x^7 + 4653x^6 - 2343x^5 + 1210x^4 - 605x^3 + 231x^2 - 44x + 10	\( -\,2^{2}\cdot 3^{21}\cdot 11^{18}\cdot 683 \)	22T37	$[2]$ (GRH)
22.0.436946304674948987202161022509859.1	x^22 - 7x^21 + 27x^20 - 73x^19 + 238x^18 - 681x^17 + 1593x^16 - 3279x^15 + 6450x^14 - 11717x^13 + 18830x^12 - 25953x^11 + 31166x^10 - 32372x^9 + 28878x^8 - 22278x^7 + 14793x^6 - 8202x^5 + 3676x^4 - 1240x^3 + 279x^2 - 40x + 4	\( -\,3^{21}\cdot 11^{19}\cdot 683 \)	22T37	$[2]$ (GRH)
22.12.43207326253951723658496833604222208442368.1	x^22 - 33x^20 + 451x^18 - 3575x^16 + 19338x^14 - 74074x^12 - 2852x^11 + 200662x^10 + 23496x^9 - 379214x^8 - 35640x^7 + 458469x^6 - 29568x^5 - 295317x^4 + 77132x^3 + 71159x^2 - 32472x + 2545	\( -\,2^{28}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.16.43207326253951723658496833604222208442368.1	x^22 - 33x^20 - 66x^19 + 231x^18 + 1144x^17 + 1529x^16 - 4928x^15 - 22154x^14 - 1936x^13 + 88242x^12 - 17636x^11 - 365706x^10 + 218944x^9 + 1743610x^8 + 775632x^7 - 2869999x^6 - 3158496x^5 + 575311x^4 + 2206182x^3 + 942403x^2 + 77528x + 1789	\( -\,2^{28}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.12.67897226970495565749066452806634898980864.1	x^22 - 22x^20 + 220x^18 - 1584x^16 + 8448x^14 - 32032x^12 - 2852x^11 + 97152x^10 + 18084x^9 - 192896x^8 + 65120x^7 + 281600x^6 - 205568x^5 - 197120x^4 + 162272x^3 + 33792x^2 - 40128x + 6044	\( -\,2^{28}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.16.67897226970495565749066452806634898980864.1	x^22 - 55x^20 - 22x^19 + 957x^18 + 198x^17 - 7293x^16 + 1914x^15 + 24794x^14 - 25828x^13 - 28380x^12 + 85584x^11 - 13596x^10 - 105028x^9 + 73260x^8 + 53592x^7 - 84535x^6 - 11374x^5 + 43571x^4 + 264x^3 - 10241x^2 + 572x + 1115	\( -\,2^{28}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.16.98759602866175368362278476809650762153984.1	x^22 - 44x^20 + 814x^18 - 8426x^16 - 176x^15 + 54912x^14 + 4752x^13 - 239844x^12 - 52324x^11 + 715836x^10 + 302192x^9 - 1393920x^8 - 959640x^7 + 1505240x^6 + 1551528x^5 - 514272x^4 - 984368x^3 - 174856x^2 + 115280x + 32136	\( -\,2^{32}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.16.172829305015806894633987334416888833769472.1	x^22 - 33x^20 + 429x^18 - 176x^17 - 4081x^16 + 5852x^15 + 47674x^14 - 68332x^13 - 459998x^12 + 333988x^11 + 2587090x^10 - 470580x^9 - 7832726x^8 - 1357004x^7 + 11956197x^6 + 4761548x^5 - 7915633x^4 - 4092132x^3 + 1244177x^2 + 607860x + 45207	\( -\,2^{30}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.12.395038411464701473449113907238603048615936.1	x^22 + 22x^20 - 1672x^16 + 308x^14 + 24904x^12 - 42020x^10 - 12672x^8 + 47916x^6 - 18128x^4 - 484x^2 + 324	\( -\,2^{34}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.12.395038411464701473449113907238603048615936.2	x^22 - 132x^18 + 5104x^14 + 704x^12 - 72512x^10 - 22528x^8 + 301312x^6 + 129536x^4 - 202752x^2 + 25600	\( -\,2^{34}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.10.691317220063227578535949337667555335077888.1	x^22 - 88x^19 - 22x^18 + 616x^17 + 1254x^16 + 286x^15 - 26026x^14 + 22704x^13 + 119592x^12 - 242466x^11 + 48444x^10 + 529892x^9 - 1135354x^8 + 428692x^7 + 1028302x^6 - 1280840x^5 + 779856x^4 - 36300x^3 - 293150x^2 + 93324x + 8730	\( 2^{32}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.14.691317220063227578535949337667555335077888.1	x^22 - 33x^20 + 275x^18 + 1485x^16 - 28666x^14 + 60214x^12 + 517242x^10 - 1742862x^8 - 1958407x^6 + 5945995x^4 + 5048131x^2 - 209503	\( 2^{32}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.10.1086355631527929051985063244906158383693824.1	x^22 + 11x^20 - 121x^18 - 935x^16 + 5258x^14 + 16830x^12 - 52690x^10 - 105182x^8 + 181093x^6 + 216359x^4 - 183909x^2 - 24299	\( 2^{32}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.14.1086355631527929051985063244906158383693824.1	x^22 - 33x^20 + 385x^18 - 2057x^16 + 6754x^14 - 18106x^12 - 3800x^11 + 27874x^10 - 19008x^9 - 43450x^8 + 58608x^7 + 18909x^6 - 30800x^5 - 2629x^4 + 4488x^3 + 253x^2 - 176x - 13	\( 2^{32}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.12.1580153645858805893796455628954412194463744.1	x^22 - 22x^20 - 44x^18 + 1892x^16 - 3740x^14 - 33968x^12 + 112464x^10 + 18480x^8 - 226336x^6 + 9152x^4 + 10032x^2 + 16	\( -\,2^{36}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.20.1580153645858805893796455628954412194463744.1	x^22 - 55x^20 + 1199x^18 - 13299x^16 + 81114x^14 - 279642x^12 + 532422x^10 - 491194x^8 + 80201x^6 + 190157x^4 - 119053x^2 + 18225	\( -\,2^{36}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.8.1580153645858805893796455628954412194463744.1	x^22 + 22x^20 - 66x^18 - 1892x^16 + 2684x^14 + 50908x^12 - 77924x^10 - 384824x^8 + 646272x^6 + 36080x^4 + 660x^2 + 4	\( -\,2^{36}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.12.1580153645858805893796455628954412194463744.2	x^22 - 11x^20 - 275x^18 + 1529x^16 + 22814x^14 - 2178x^12 - 137698x^10 + 20262x^8 + 180081x^6 - 29315x^4 + 517x^2 + 1	\( -\,2^{36}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.4.1620949848995907632875795273183398788595712.1	x^22 + 22x^20 - 44x^19 + 308x^18 - 682x^17 + 5148x^16 - 4884x^15 + 20746x^14 - 37576x^13 + 458128x^12 + 582788x^11 + 2492600x^10 - 5616732x^9 + 12766776x^8 + 72829196x^7 + 27797264x^6 - 125806824x^5 - 187011000x^4 - 118806292x^3 - 39878476x^2 - 6794304x - 306180	\( -\,2^{22}\cdot 7^{15}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.12.2765268880252910314143797350670221340311552.1	x^22 - 33x^20 + 33x^18 + 3751x^16 + 16654x^14 + 4818x^12 - 68354x^10 - 35706x^8 + 96261x^6 + 1683x^4 - 13079x^2 + 1183	\( -\,2^{34}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.10.2765268880252910314143797350670221340311552.1	x^22 - 33x^20 - 66x^19 + 319x^18 + 1342x^17 + 275x^16 - 6336x^15 - 7546x^14 + 18568x^13 + 44792x^12 - 23260x^11 - 155342x^10 - 59884x^9 + 294888x^8 + 78716x^7 - 1479335x^6 - 3296436x^5 - 3200659x^4 - 1325390x^3 - 1397x^2 + 107514x + 585	\( 2^{34}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.14.2765268880252910314143797350670221340311552.1	x^22 - 33x^20 + 99x^18 + 6941x^16 - 92950x^14 + 428230x^12 - 610082x^10 - 138182x^8 + 643797x^6 - 67749x^4 - 94897x^2 - 567	\( 2^{34}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.18.2765268880252910314143797350670221340311552.1	x^22 - 22x^20 - 88x^18 + 3520x^16 - 4576x^14 - 99132x^12 + 468424x^10 - 870980x^8 + 806696x^6 - 380600x^4 + 81092x^2 - 4732	\( 2^{34}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.14.2765268880252910314143797350670221340311552.2	x^22 - 33x^20 + 99x^18 + 4125x^16 - 15862x^14 - 109450x^12 + 423302x^10 - 148038x^8 - 370491x^6 + 88539x^4 + 3399x^2 - 7	\( 2^{34}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.10.4345422526111716207940252979624633534775296.1	x^22 - 33x^20 + 231x^18 + 1353x^16 - 13310x^14 + 11374x^12 + 75878x^10 - 61974x^8 - 132979x^6 - 51997x^4 - 4829x^2 - 99	\( 2^{34}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.18.4345422526111716207940252979624633534775296.1	x^22 - 44x^20 + 660x^18 - 2640x^16 - 27456x^14 + 312576x^12 - 1046848x^10 + 991232x^8 + 892672x^6 - 1402368x^4 + 259072x^2 - 11264	\( 2^{34}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.12.6320614583435223575185822515817648777854976.1	x^22 - 220x^18 - 506x^16 + 6380x^14 + 14916x^12 - 26136x^10 - 44396x^8 + 40700x^6 + 30140x^4 - 24728x^2 + 2500	\( -\,2^{38}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.20.6320614583435223575185822515817648777854976.1	x^22 - 55x^20 + 1177x^18 - 12639x^16 + 73898x^14 - 237402x^12 + 390258x^10 - 246906x^8 - 33011x^6 + 40249x^4 - 451x^2 + 1	\( -\,2^{38}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.8.6320614583435223575185822515817648777854976.1	x^22 + 22x^20 - 22x^18 - 1738x^16 + 1100x^14 + 22000x^12 + 4840x^10 - 87120x^8 - 57596x^6 + 104544x^4 + 94380x^2 + 484	\( -\,2^{38}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.12.6320614583435223575185822515817648777854976.2	x^22 - 132x^18 - 66x^16 + 4840x^14 + 4312x^12 - 43648x^10 - 24156x^8 + 144188x^6 + 10736x^4 - 162668x^2 + 66564	\( -\,2^{38}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.10.11061075521011641256575189402680885361246208.1	x^22 + 11x^20 - 341x^18 + 693x^16 + 6402x^14 - 5434x^12 - 36850x^10 - 27742x^8 + 3245x^6 + 4191x^4 + 407x^2 - 7	\( 2^{36}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.14.11061075521011641256575189402680885361246208.1	x^22 - 264x^18 + 748x^16 + 7304x^14 - 24640x^12 - 37488x^10 + 183568x^8 - 139744x^6 + 1408x^4 + 22528x^2 - 4032	\( 2^{36}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.14.11061075521011641256575189402680885361246208.2	x^22 - 22x^20 - 22x^19 + 44x^18 + 1100x^17 - 264x^16 - 7964x^15 - 9768x^14 + 45496x^13 + 143198x^12 - 386424x^11 - 452100x^10 + 1638604x^9 + 70312x^8 - 2908488x^7 + 1303676x^6 + 2055152x^5 - 1542332x^4 - 334400x^3 + 455400x^2 - 72072x + 2060	\( 2^{36}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.14.11061075521011641256575189402680885361246208.3	x^22 - 33x^20 + 363x^18 - 484x^17 - 2959x^16 + 7524x^15 + 27676x^14 - 19228x^13 - 69872x^12 + 263964x^11 + 670384x^10 - 603768x^9 - 3185732x^8 - 2479356x^7 + 1671351x^6 + 2734556x^5 + 459613x^4 - 635404x^3 - 289971x^2 - 21428x + 4351	\( 2^{36}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.10.17381690104446864831761011918498534139101184.1	x^22 - 11x^20 - 253x^18 + 77x^16 + 15290x^14 + 78210x^12 + 137742x^10 + 50710x^8 - 38687x^6 + 4301x^4 + 11x^2 - 11	\( 2^{36}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.14.17381690104446864831761011918498534139101184.1	x^22 - 11x^20 - 451x^18 + 8921x^16 - 51810x^14 + 88154x^12 + 94710x^10 - 303358x^8 + 111265x^6 + 50193x^4 + 253x^2 - 539	\( 2^{36}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.12.25282458333740894300743290063270595111419904.1	x^22 - 11x^20 - 99x^18 + 737x^16 + 4444x^14 - 3982x^12 - 26972x^10 + 16874x^8 + 27203x^6 - 8283x^4 - 165x^2 + 1	\( -\,2^{40}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.8.25282458333740894300743290063270595111419904.1	x^22 - 11x^20 - 297x^18 + 1639x^16 + 20130x^14 + 39776x^12 + 10890x^10 - 19096x^8 - 10527x^6 + 231x^4 + 715x^2 + 49	\( -\,2^{40}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.8.44244302084046565026300757610723541444984832.1	x^22 + 44x^20 + 330x^18 - 1122x^16 - 10428x^14 - 9548x^12 + 33044x^10 + 58124x^8 + 25432x^6 + 748x^4 - 836x^2 + 28	\( -\,2^{38}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.10.44244302084046565026300757610723541444984832.1	x^22 + 33x^20 + 319x^18 - 209x^16 - 20988x^14 - 118448x^12 - 163020x^10 + 383460x^8 + 725043x^6 - 627737x^4 + 111749x^2 - 7	\( 2^{38}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.10.44244302084046565026300757610723541444984832.2	x^22 - 22x^20 - 88x^18 + 2200x^16 + 13420x^14 - 3476x^12 - 167728x^10 - 311784x^8 + 46288x^6 + 308176x^4 - 55088x^2 - 2800	\( 2^{38}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.10.69526760417787459327044047673994136556404736.1	x^22 - 11x^20 - 121x^18 + 1507x^16 + 484x^14 - 38368x^12 + 43252x^10 + 304084x^8 - 258445x^6 - 918269x^4 - 344355x^2 - 3179	\( 2^{38}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.10.69526760417787459327044047673994136556404736.2	x^22 - 11x^20 - 55x^18 + 737x^16 + 946x^14 - 14982x^12 - 7326x^10 + 87538x^8 + 66957x^6 - 46255x^4 - 16203x^2 - 275	\( 2^{38}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.12.103740790335738088504050897483737522470125568.1	x^22 - 44x^20 - 88x^19 + 660x^18 + 2618x^17 - 3058x^16 - 26224x^15 + 17820x^14 + 233288x^13 - 204908x^12 - 2903728x^11 - 3647732x^10 + 10497784x^9 + 34411080x^8 + 26459576x^7 - 25406876x^6 - 57398352x^5 - 33631884x^4 - 3176272x^3 + 1810160x^2 - 799480x - 456124	\( -\,2^{28}\cdot 7^{15}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.8.176977208336186260105203030442894165779939328.1	x^22 - 440x^18 + 1760x^16 + 29216x^14 - 54208x^12 - 381568x^10 + 2816x^8 + 1143296x^6 + 1216512x^4 + 405504x^2 + 28672	\( -\,2^{40}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.22.707908833344745040420812121771576663119757312.1	x^22 - 55x^20 + 1199x^18 - 13959x^16 + 96910x^14 - 420420x^12 + 1158014x^10 - 2018390x^8 + 2176097x^6 - 1379961x^4 + 464013x^2 - 63175	\( 2^{42}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.22.1112428166684599349232704762783906184902475776.1	x^22 - 55x^20 + 1155x^18 - 12859x^16 + 85866x^14 - 363440x^12 + 997370x^10 - 1777446x^8 + 2018885x^6 - 1393997x^4 + 527813x^2 - 83259	\( 2^{42}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.6.3842933666728615933712980089617130456935825408.1	x^22 + 22x^20 + 198x^18 + 924x^16 + 2288x^14 + 2464x^12 - 616x^10 - 3344x^8 - 1232x^6 + 1056x^4 + 352x^2 - 152	\( 2^{43}\cdot 7^{10}\cdot 11^{22}\cdot 19 \)	22T37	Trivial (GRH)