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 90)

Label	Polynomial	Discriminant	Galois group	Class group
18.16.13281973786033764243536179.1	x^18 - 9x^17 + 25x^16 + 4x^15 - 137x^14 + 175x^13 + 179x^12 - 515x^11 + 116x^10 + 542x^9 - 442x^8 - 181x^7 + 375x^6 - 49x^5 - 136x^4 + 35x^3 + 20x^2 - 3x - 1	\( -\,67\cdot 2113\cdot 9685993193^{2} \)	18T968	Trivial (GRH)
18.16.36374607805480156224815104.1	x^18 - 11x^16 + 39x^14 - 29x^12 - 110x^10 + 246x^8 - 204x^6 + 81x^4 - 15x^2 + 1	\( -\,2^{18}\cdot 11779563529^{2} \)	18T968	Trivial (GRH)
18.16.70853239618582582520971264.1	x^18 - 14x^16 + 67x^14 - 125x^12 + 12x^10 + 272x^8 - 366x^6 + 190x^4 - 37x^2 + 1	\( -\,2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T764	Trivial (GRH)
18.16.70853239618582582520971264.2	x^18 - 9x^16 + 21x^14 + 25x^12 - 182x^10 + 303x^8 - 229x^6 + 85x^4 - 15x^2 + 1	\( -\,2^{18}\cdot 37^{4}\cdot 229^{6} \)	18T764	Trivial (GRH)
18.16.75613185918270483380568064.1	x^18 - 14x^16 + 66x^14 - 134x^12 + 91x^10 + 78x^8 - 159x^6 + 87x^4 - 18x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T460	Trivial (GRH)
18.16.80421398252924334225227776.1	x^18 - 10x^16 + 21x^14 + 67x^12 - 362x^10 + 621x^8 - 495x^6 + 183x^4 - 26x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.16.80421398252924334225227776.2	x^18 - 14x^16 + 77x^14 - 211x^12 + 294x^10 - 168x^8 - 30x^6 + 70x^4 - 21x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.16.104192253035948620552339456.1	x^18 - 12x^16 + 48x^14 - 59x^12 - 61x^10 + 206x^8 - 183x^6 + 74x^4 - 14x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T879	Trivial (GRH)
18.16.104192253035948620552339456.2	x^18 - 15x^16 + 83x^14 - 202x^12 + 168x^10 + 150x^8 - 365x^6 + 207x^4 - 27x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T879	Trivial (GRH)
18.16.258151783382020583032356864.1	x^18 - 9x^16 + 9x^14 + 96x^12 - 333x^10 + 450x^8 - 306x^6 + 108x^4 - 18x^2 + 1	\( -\,2^{18}\cdot 3^{44} \)	18T460	Trivial (GRH)
18.16.354293866282050926558838784.1	x^18 - 10x^16 + 29x^14 + 8x^12 - 188x^10 + 361x^8 - 292x^6 + 109x^4 - 18x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.16.354293866282050926558838784.2	x^18 - 10x^16 + 9x^14 + 144x^12 - 513x^10 + 724x^8 - 512x^6 + 184x^4 - 29x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.16.426335653934475248756850688.1	x^18 - 17x^16 + 77x^14 + 136x^12 - 2044x^10 + 6119x^8 - 8033x^6 + 4835x^4 - 1110x^2 + 37	\( -\,2^{24}\cdot 37^{7}\cdot 16361^{2} \)	18T912	Trivial (GRH)
18.16.737445455454227457309147136.1	x^18 - 12x^16 + 53x^14 - 91x^12 - 27x^10 + 318x^8 - 428x^6 + 213x^4 - 27x^2 + 1	\( -\,2^{30}\cdot 37^{6}\cdot 16361^{2} \)	18T912	Trivial (GRH)
18.16.1024770265180753855691096064.1	x^18 - 12x^16 + 42x^14 - 11x^12 - 243x^10 + 579x^8 - 559x^6 + 234x^4 - 33x^2 + 1	\( -\,2^{18}\cdot 3^{24}\cdot 7^{12} \)	18T459	Trivial (GRH)
18.16.3520799260895172463279296875.1	x^18 - 17x^16 - 6x^15 + 113x^14 + 85x^13 - 353x^12 - 452x^11 + 422x^10 + 1084x^9 + 287x^8 - 1014x^7 - 1060x^6 - 61x^5 + 507x^4 + 362x^3 + 113x^2 + 17x + 1	\( -\,5^{9}\cdot 7^{12}\cdot 41\cdot 419\cdot 1399\cdot 5419 \)	18T857	Trivial (GRH)
18.16.5218730914804258637835403264.1	x^18 - 22x^16 + 173x^14 - 545x^12 + 279x^10 + 1788x^8 - 3122x^6 + 1509x^4 - 91x^2 + 1	\( -\,2^{24}\cdot 19^{6}\cdot 137^{6} \)	18T691	Trivial (GRH)
18.16.7106493786222379509303476224.1	x^18 - 20x^16 + 156x^14 - 602x^12 + 1204x^10 - 1197x^8 + 504x^6 - 24x^4 - 24x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.16.7106493786222379509303476224.2	x^18 - 17x^16 + 109x^14 - 329x^12 + 462x^10 - 217x^8 - 84x^6 + 93x^4 - 20x^2 + 1	\( -\,2^{18}\cdot 7^{16}\cdot 13^{8} \)	18T586	Trivial (GRH)
18.16.17171174753799627467382181888.1	x^18 - 25x^16 + 246x^14 - 1245x^12 + 3470x^10 - 5082x^8 + 2731x^6 + 1768x^4 - 2704x^2 + 832	\( -\,2^{12}\cdot 7^{12}\cdot 13^{13} \)	18T459	Trivial (GRH)
18.16.22563186417495171794318638244.1	x^18 - 27x^16 + 190x^14 - 305x^12 - 1406x^10 + 6214x^8 - 8812x^6 + 4829x^4 - 853x^2 + 41	\( -\,2^{2}\cdot 37^{4}\cdot 41\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial (GRH)
18.16.35675388820222120719231418368.1	x^18 - 6x^17 + 6x^16 + 38x^15 - 184x^14 + 390x^13 + 275x^12 - 3166x^11 + 4308x^10 + 3710x^9 - 13016x^8 + 7380x^7 + 5183x^6 - 7128x^5 + 2214x^4 + 150x^3 - 170x^2 + 24x - 1	\( -\,2^{16}\cdot 3^{9}\cdot 37^{6}\cdot 47^{6} \)	18T623	Trivial (GRH)
18.16.44202745482204952292385377971.1	x^18 - 21x^16 - 6x^15 + 178x^14 + 105x^13 - 762x^12 - 712x^11 + 1627x^10 + 2311x^9 - 1158x^8 - 3464x^7 - 1237x^6 + 1514x^5 + 1732x^4 + 771x^3 + 178x^2 + 21x + 1	\( -\,7^{12}\cdot 71\cdot 181^{3}\cdot 7585403561 \)	18T926	Trivial (GRH)
18.16.45693926947235862150060703744.1	x^18 - 11x^16 + 8x^14 + 413x^12 - 2634x^10 + 7683x^8 - 12405x^6 + 11296x^4 - 5376x^2 + 1024	\( -\,2^{24}\cdot 37^{6}\cdot 101^{6} \)	18T623	Trivial (GRH)
18.16.46565137128897741068083984375.1	x^18 - 21x^16 - 6x^15 + 178x^14 + 105x^13 - 763x^12 - 712x^11 + 1637x^10 + 2314x^9 - 1189x^8 - 3484x^7 - 1210x^6 + 1545x^5 + 1742x^4 + 772x^3 + 178x^2 + 21x + 1	\( -\,5^{9}\cdot 89\cdot 3881^{3}\cdot 4582578491 \)	18T951	Trivial (GRH)
18.16.70102248494107553872773644288.1	x^18 - 24x^16 - 6x^15 + 234x^14 + 120x^13 - 1169x^12 - 936x^11 + 3031x^10 + 3532x^9 - 3260x^8 - 6302x^7 - 866x^6 + 3728x^5 + 3151x^4 + 1178x^3 + 234x^2 + 24x + 1	\( -\,2^{18}\cdot 127\cdot 257^{6}\cdot 7307849 \)	18T930	Trivial (GRH)
18.16.78517044906553135777336648704.1	x^18 - 27x^16 + 186x^14 - 399x^12 - 333x^10 + 2511x^8 - 3717x^6 + 2430x^4 - 729x^2 + 81	\( -\,2^{10}\cdot 3^{22}\cdot 367^{6} \)	18T882	Trivial (GRH)
18.16.95564557288413087196109602816.1	x^18 - 13x^16 - 8x^14 + 506x^12 - 1867x^10 + 2559x^8 - 1411x^6 + 327x^4 - 31x^2 + 1	\( -\,2^{30}\cdot 2113^{6} \)	18T691	Trivial (GRH)
18.16.111573680909827761716592640000.1	x^18 - 21x^16 + 178x^14 - 793x^12 + 2006x^10 - 2873x^8 + 2141x^6 - 616x^4 - 40x^2 + 16	\( -\,2^{22}\cdot 5^{4}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.16.114805789186292807734226138688.1	x^18 - 6x^16 - 72x^14 + 921x^12 - 4239x^10 + 10089x^8 - 12951x^6 + 8208x^4 - 1881x^2 + 57	\( -\,2^{6}\cdot 3^{33}\cdot 19^{9} \)	18T585	Trivial (GRH)
18.16.139467101137284702145740800000.1	x^18 - 9x^16 - 26x^14 + 495x^12 - 1922x^10 + 3399x^8 - 3079x^6 + 1420x^4 - 300x^2 + 20	\( -\,2^{20}\cdot 5^{5}\cdot 37^{8}\cdot 59^{4} \)	18T772	Trivial (GRH)
18.16.255949408201806577166482421875.1	x^18 - 23x^16 - 6x^15 + 212x^14 + 115x^13 - 982x^12 - 848x^11 + 2281x^10 + 2971x^9 - 1932x^8 - 4792x^7 - 1355x^6 + 2356x^5 + 2396x^4 + 991x^3 + 212x^2 + 23x + 1	\( -\,5^{9}\cdot 31\cdot 139^{6}\cdot 8951\cdot 65479 \)	18T915	Trivial (GRH)
18.16.350896807924550394793668620288.1	x^18 - 21x^16 - 6x^15 + 178x^14 + 105x^13 - 762x^12 - 712x^11 + 1626x^10 + 2311x^9 - 1151x^8 - 3462x^7 - 1247x^6 + 1507x^5 + 1731x^4 + 771x^3 + 178x^2 + 21x + 1	\( -\,2^{12}\cdot 37^{9}\cdot 4799\cdot 137357761 \)	18T874	Trivial (GRH)
18.16.386714237259091562894235414528.1	x^18 - 33x^16 + 423x^14 - 2733x^12 + 9531x^10 - 17685x^8 + 16020x^6 - 5760x^4 + 369x^2 + 3	\( -\,2^{12}\cdot 3^{33}\cdot 19^{8} \)	18T585	Trivial (GRH)
18.16.409666032821894048413630669979.1	x^18 - 18x^16 - 6x^15 + 129x^14 + 90x^13 - 451x^12 - 516x^11 + 699x^10 + 1378x^9 - 19x^8 - 1578x^7 - 1138x^6 + 277x^5 + 789x^4 + 460x^3 + 129x^2 + 18x + 1	\( -\,23\cdot 79^{3}\cdot 3391\cdot 15227^{3}\cdot 3017519 \)	18T962	Trivial (GRH)
18.16.563529338817440388228836233216.1	x^18 - 16x^16 + 91x^14 - 228x^12 + 234x^10 - 181x^6 + 135x^4 - 39x^2 + 4	\( -\,2^{12}\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial (GRH)
18.16.691976677792049302709773533184.1	x^18 - 20x^16 + 157x^14 - 628x^12 + 1403x^10 - 1789x^8 + 1258x^6 - 435x^4 + 53x^2 + 1	\( -\,2^{18}\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.16.691976677792049302709773533184.2	x^18 - 18x^16 + 125x^14 - 412x^12 + 617x^10 - 255x^8 - 177x^6 + 121x^4 - 20x^2 + 1	\( -\,2^{18}\cdot 1129^{8} \)	18T548	Trivial (GRH)
18.16.706653404158978221996029838336.1	x^18 - 36x^16 + 363x^14 - 1710x^12 + 4317x^10 - 5898x^8 + 3858x^6 - 585x^4 - 315x^2 + 9	\( -\,2^{10}\cdot 3^{24}\cdot 367^{6} \)	18T882	$[2]$ (GRH)
18.16.761214556722353601306276827136.1	x^18 - 33x^16 + 414x^14 - 2506x^12 + 7476x^10 - 9492x^8 + 2527x^6 - 153x^4 - 12x^2 + 1	\( -\,2^{12}\cdot 3^{18}\cdot 7^{14}\cdot 29^{4} \)	18T766	Trivial (GRH)
18.16.1322190894838063508462575484928.1	x^18 - 24x^16 + 180x^14 - 351x^12 - 1620x^10 + 9072x^8 - 16497x^6 + 12960x^4 - 3888x^2 + 243	\( -\,2^{16}\cdot 3^{25}\cdot 47^{8} \)	18T881	Trivial (GRH)
18.16.2414477422103715329143346811072.1	x^18 - 6x^17 - 27x^16 + 225x^15 + 99x^14 - 2883x^13 + 1709x^12 + 17955x^11 - 13251x^10 - 79555x^9 + 48447x^8 + 296877x^7 - 264292x^6 - 523467x^5 + 683256x^4 + 173607x^3 - 426153x^2 + 7056x + 78253	\( -\,2^{6}\cdot 3^{18}\cdot 7^{15}\cdot 29^{5} \)	18T766	Trivial (GRH)
18.16.3258180556352735703113612132352.1	x^18 - 33x^16 - 4x^15 + 447x^14 + 96x^13 - 3317x^12 - 1032x^11 + 15000x^10 + 6720x^9 - 41586x^8 - 26076x^7 + 63828x^6 + 50472x^5 - 44976x^4 - 38968x^3 + 13200x^2 + 9096x - 2276	\( -\,2^{26}\cdot 3^{24}\cdot 37^{6}\cdot 67 \)	18T734	Trivial (GRH)
18.16.3264114697598096618126654891659.1	x^18 - 23x^16 - 6x^15 + 213x^14 + 115x^13 - 999x^12 - 852x^11 + 2381x^10 + 3022x^9 - 2164x^8 - 4992x^7 - 1216x^6 + 2590x^5 + 2496x^4 + 1008x^3 + 213x^2 + 23x + 1	\( -\,11^{6}\cdot 13^{3}\cdot 43^{7}\cdot 45337\cdot 68053 \)	18T945	Trivial (GRH)
18.16.3426722037220245220088000000000.1	x^18 - 17x^16 - 6x^15 + 110x^14 + 85x^13 - 316x^12 - 440x^11 + 256x^10 + 973x^9 + 591x^8 - 682x^7 - 1177x^6 - 371x^5 + 341x^4 + 325x^3 + 110x^2 + 17x + 1	\( -\,2^{12}\cdot 5^{9}\cdot 37^{6}\cdot 166946971879 \)	18T903	Trivial (GRH)
18.16.3695846601235939006516933165056.1	x^18 - 6x^17 - 15x^16 + 170x^15 - 186x^14 - 1392x^13 + 4226x^12 + 678x^11 - 20544x^10 + 29008x^9 + 12396x^8 - 66546x^7 + 50014x^6 + 16776x^5 - 41670x^4 + 19786x^3 - 2589x^2 - 114x - 1	\( -\,2^{28}\cdot 3^{24}\cdot 19\cdot 37^{6} \)	18T734	Trivial (GRH)
18.16.4405473434934059943108359950336.1	x^18 - 17x^16 + 72x^14 + 143x^12 - 1593x^10 + 3357x^8 - 2463x^6 + 608x^4 - 48x^2 + 1	\( -\,2^{12}\cdot 32009^{6} \)	18T662	Trivial (GRH)
18.16.4405473434934059943108359950336.2	x^18 - 12x^16 + 15x^14 + 380x^12 - 2294x^10 + 5736x^8 - 7145x^6 + 4236x^4 - 944x^2 + 64	\( -\,2^{12}\cdot 32009^{6} \)	18T662	Trivial (GRH)
18.16.10591557210270270882668865220943.1	x^18 - 41x^16 + 706x^14 - 6650x^12 + 37313x^10 - 126731x^8 + 250624x^6 - 254274x^4 + 86032x^2 + 15023	\( -\,7^{12}\cdot 83^{5}\cdot 181^{5} \)	18T839	Trivial (GRH)
18.16.10914998836481629364809687506111.1	x^18 - 9x^17 + 18x^16 + 60x^15 - 253x^14 + 7x^13 + 1019x^12 - 823x^11 - 1809x^10 + 2313x^9 + 1408x^8 - 2719x^7 - 213x^6 + 1477x^5 - 276x^4 - 336x^3 + 114x^2 + 21x - 9	\( -\,3^{8}\cdot 7\cdot 53^{4}\cdot 107^{8}\cdot 1753 \)	18T881	Trivial (GRH)