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 43 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.139332652309974923829.1	x^18 - 7x^17 + 21x^16 - 35x^15 + 41x^14 - 54x^13 + 81x^12 - 80x^11 + 28x^10 + 12x^9 + 7x^8 - 14x^7 - 33x^6 + 46x^5 - 3x^4 - 27x^3 + 21x^2 - 7x + 1	\( 3^{6}\cdot 29\cdot 433^{6} \)	18T691	Trivial
18.2.427607105365095455889.1	x^18 - 9x^17 + 40x^16 - 116x^15 + 246x^14 - 406x^13 + 547x^12 - 630x^11 + 638x^10 - 561x^9 + 401x^8 - 202x^7 + 50x^6 + 7x^5 - 7x^4 + x^3 + 4x^2 - 4x + 1	\( 3^{6}\cdot 89\cdot 433^{6} \)	18T691	Trivial
18.0.894396879913401450496.3	x^18 + 2x^16 + x^14 + 9x^12 + 23x^10 + 2x^8 - 20x^6 + 13x^4 - 3x^2 + 1	\( -\,2^{30}\cdot 97^{6} \)	18T691	Trivial (GRH)
18.4.3761981612369322943383.1	x^18 - x^17 + x^16 + x^15 - 19x^14 + 22x^13 - 8x^12 - 18x^11 + 76x^10 - 50x^9 - 8x^8 + 45x^7 - 73x^6 + 40x^5 - 20x^4 + 4x^3 + 2x^2 - x + 1	\( -\,3^{9}\cdot 29\cdot 433^{6} \)	18T691	Trivial (GRH)
18.4.11545391844857577309003.1	x^18 - 4x^17 + 4x^16 + 8x^15 - 24x^14 + 17x^13 + 21x^12 - 66x^11 + 56x^10 + 58x^9 - 156x^8 + 30x^7 + 168x^6 - 92x^5 - 90x^4 + 77x^3 + 23x^2 - 31x - 5	\( -\,3^{9}\cdot 89\cdot 433^{6} \)	18T691	Trivial (GRH)
18.0.12539558025308224000000.1	x^18 + 6x^16 + 21x^14 + 35x^12 + 38x^10 + 32x^8 + 2x^6 + 2x^4 - 5x^2 + 1	\( -\,2^{12}\cdot 5^{6}\cdot 241^{6} \)	18T691	Trivial (GRH)
18.0.19679535995229561655296.1	x^18 - 2x^16 + 2x^14 + 12x^12 + 7x^10 + 29x^8 + 14x^6 + 17x^4 + 8x^2 + 1	\( -\,2^{12}\cdot 3^{6}\cdot 433^{6} \)	18T691	Trivial (GRH)
18.2.26747587516386219015625.1	x^18 - 9x^17 + 44x^16 - 148x^15 + 378x^14 - 770x^13 + 1290x^12 - 1812x^11 + 2162x^10 - 2208x^9 + 1936x^8 - 1454x^7 + 929x^6 - 499x^5 + 223x^4 - 82x^3 + 26x^2 - 7x + 1	\( 5^{6}\cdot 241^{6}\cdot 8737 \)	18T691	Trivial (GRH)
18.6.44926056388705565802496.1	x^18 - 9x^17 + 35x^16 - 76x^15 + 98x^14 - 70x^13 + 10x^12 + 44x^11 - 79x^10 + 87x^9 - 57x^8 + 8x^7 + 22x^6 - 22x^5 + 12x^4 - 6x^3 + 3x^2 - x - 1	\( 2^{20}\cdot 193^{6}\cdot 829 \)	18T691	Trivial (GRH)
18.6.531347471871198164692992.2	x^18 - 10x^16 + 37x^14 - 56x^12 + x^10 + 105x^8 - 110x^6 - 12x^4 + 72x^2 - 27	\( 2^{12}\cdot 3^{9}\cdot 433^{6} \)	18T691	Trivial (GRH)
18.0.718816902219289052839936.1	x^18 - 2x^17 + 5x^16 - 18x^15 + 27x^14 - 16x^13 + 43x^12 - 142x^11 + 202x^10 - 186x^9 + 260x^8 - 416x^7 + 382x^6 - 116x^5 - 76x^4 + 48x^3 + 40x^2 - 48x + 16	\( -\,2^{24}\cdot 193^{6}\cdot 829 \)	18T691	$[2]$ (GRH)
18.2.3343448439548277376953125.1	x^18 - 5x^17 + 6x^16 - 2x^15 + 15x^14 - 10x^13 - 58x^12 + 115x^11 - 182x^10 + 227x^9 + 178x^8 - 804x^7 + 685x^6 - 46x^5 - 356x^4 + 581x^3 - 584x^2 + 304x - 64	\( 5^{9}\cdot 241^{6}\cdot 8737 \)	18T691	$[2]$ (GRH)
18.8.34400814135672603325575168.2	x^18 - 7x^17 + 7x^16 + 66x^15 - 213x^14 + 51x^13 + 786x^12 - 1415x^11 + 404x^10 + 1577x^9 - 2390x^8 + 1649x^7 - 576x^6 - 35x^5 + 173x^4 - 108x^3 + 39x^2 - 9x + 1	\( -\,2^{12}\cdot 3^{3}\cdot 19^{6}\cdot 137^{6} \)	18T691	Trivial (GRH)
18.8.59882898680615272455630848.1	x^18 - 4x^16 - 40x^14 + 75x^12 + 524x^10 + 309x^8 - 724x^6 - 491x^4 + 239x^2 + 47	\( -\,2^{12}\cdot 19^{6}\cdot 47\cdot 137^{6} \)	18T691	Trivial (GRH)
18.10.67527524044098073194647552.1	x^18 - x^17 - 20x^16 + 9x^15 + 141x^14 - 23x^13 - 418x^12 + 110x^11 + 623x^10 - 293x^9 - 407x^8 + 299x^7 + 26x^6 - 68x^5 + 38x^4 - 32x^3 + 16x^2 - x - 1	\( 2^{12}\cdot 19^{6}\cdot 53\cdot 137^{6} \)	18T691	Trivial (GRH)
18.6.67527524044098073194647552.1	x^18 + 11x^16 + 28x^14 - 57x^12 - 253x^10 - 9x^8 + 463x^6 + 246x^4 - 84x^2 - 53	\( 2^{12}\cdot 19^{6}\cdot 53\cdot 137^{6} \)	18T691	Trivial (GRH)
18.4.75172149407580873933664256.1	x^18 - 7x^17 + 18x^16 - 12x^15 - 32x^14 + 62x^13 - 85x^12 + 492x^11 - 1589x^10 + 2451x^9 - 2056x^8 + 1816x^7 - 3253x^6 + 4053x^5 - 2637x^4 + 1622x^3 - 1858x^2 + 1192x - 239	\( -\,2^{12}\cdot 19^{6}\cdot 59\cdot 137^{6} \)	18T691	Trivial (GRH)
18.10.77720357862075140846669824.1	x^18 - 8x^17 + 16x^16 + 23x^15 - 126x^14 + 148x^13 + 16x^12 - 158x^11 + 78x^10 + 21x^9 + 78x^8 - 158x^7 + 16x^6 + 148x^5 - 126x^4 + 23x^3 + 16x^2 - 8x + 1	\( 2^{12}\cdot 19^{6}\cdot 61\cdot 137^{6} \)	18T691	Trivial (GRH)
18.12.81542670543816541216178176.1	x^18 - 7x^16 - 2x^15 + 16x^14 + 18x^13 - 62x^12 - 2x^11 + 254x^10 - 274x^9 - 213x^8 + 578x^7 - 457x^6 - 182x^5 + 581x^4 - 226x^3 - 34x^2 + 18x + 1	\( -\,2^{18}\cdot 19^{6}\cdot 137^{6} \)	18T691	Trivial (GRH)
18.12.81542670543816541216178176.2	x^18 - 10x^16 + 19x^14 + 81x^12 - 276x^10 - 12x^8 + 640x^6 - 416x^4 - 64x^2 + 64	\( -\,2^{18}\cdot 19^{6}\cdot 137^{6} \)	18T691	Trivial (GRH)
18.8.100654233952523543063719936.1	x^18 - 2x^17 - 5x^16 + 18x^15 - 8x^14 - 30x^13 + 51x^12 - 36x^11 + 65x^10 - 68x^9 - 367x^8 + 768x^7 + 117x^6 - 1274x^5 + 614x^4 + 674x^3 - 562x^2 - 36x + 79	\( -\,2^{12}\cdot 19^{6}\cdot 79\cdot 137^{6} \)	18T691	Trivial (GRH)
18.10.123588110042971945280770048.1	x^18 - 5x^17 - 4x^16 + 49x^15 - 41x^14 - 179x^13 + 318x^12 + 306x^11 - 754x^10 + 59x^9 + 1200x^8 - 107x^7 - 96x^6 + 1176x^5 + 194x^4 - 1151x^3 - 871x^2 - 228x - 19	\( 2^{12}\cdot 19^{6}\cdot 97\cdot 137^{6} \)	18T691	Trivial (GRH)
18.6.123588110042971945280770048.1	x^18 - 7x^17 + 18x^16 - x^15 - 119x^14 + 373x^13 - 605x^12 + 555x^11 - 153x^10 - 285x^9 + 531x^8 - 355x^7 + 259x^6 + 135x^5 + 121x^4 + 121x^3 - 52x^2 - 24x - 1	\( 2^{12}\cdot 19^{6}\cdot 97\cdot 137^{6} \)	18T691	Trivial (GRH)
18.8.207678989041282753409953792.1	x^18 - 4x^17 - 10x^16 + 70x^15 - 28x^14 - 435x^13 + 723x^12 + 861x^11 - 3348x^10 + 1562x^9 + 5405x^8 - 8077x^7 + 467x^6 + 8044x^5 - 7102x^4 + 668x^3 + 2192x^2 - 1240x + 232	\( -\,2^{12}\cdot 19^{6}\cdot 137^{6}\cdot 163 \)	18T691	Trivial (GRH)
18.4.212775405950271287235964928.1	x^18 - 7x^17 + 21x^16 - 51x^15 + 93x^14 - 153x^13 + 252x^12 - 420x^11 + 707x^10 - 1049x^9 + 1414x^8 - 1680x^7 + 2016x^6 - 2448x^5 + 2976x^4 - 3264x^3 + 2688x^2 - 1792x + 512	\( -\,2^{12}\cdot 19^{6}\cdot 137^{6}\cdot 167 \)	18T691	Trivial (GRH)
18.8.243353907404202490192031744.1	x^18 - 7x^17 + 13x^16 - 11x^15 + 39x^14 + x^13 - 178x^12 + 67x^11 - 45x^10 + 395x^9 + 299x^8 - 1209x^7 + 508x^6 + 779x^5 - 1021x^4 + 287x^3 + 309x^2 - 269x + 61	\( -\,2^{12}\cdot 19^{6}\cdot 137^{6}\cdot 191 \)	18T691	Trivial (GRH)
18.8.1493196207631454487439212544.1	x^18 - 9x^16 - 6x^15 + 39x^14 + 42x^13 - 80x^12 - 138x^11 + 33x^10 + 192x^9 + 113x^8 - 20x^7 - 106x^6 - 106x^5 + 10x^4 + 20x^3 - 17x^2 + 10x + 11	\( -\,2^{24}\cdot 2113^{6} \)	18T691	Trivial (GRH)
18.12.3316493303524288387276746752.1	x^18 - 2x^17 - 17x^16 + 36x^15 + 87x^14 - 203x^13 - 150x^12 + 295x^11 + 554x^10 + 115x^9 - 3330x^8 + 2497x^7 + 4678x^6 - 7669x^5 + 2013x^4 + 1967x^3 - 569x^2 - 285x - 19	\( -\,2^{12}\cdot 19^{7}\cdot 137^{7} \)	18T691	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)
18.16.95564557288413087196109602816.1	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)
18.12.99155887381280914118872662016.1	x^18 - 3x^16 - 25x^14 + 76x^12 + 151x^10 - 480x^8 - 31x^6 + 340x^4 - 152x^2 + 19	\( -\,2^{24}\cdot 19^{7}\cdot 137^{6} \)	18T691	Trivial (GRH)
18.0.125651828543540250519815163904.1	x^18 + 28x^16 + 243x^14 + 1019x^12 + 2373x^10 + 3184x^8 + 2379x^6 + 863x^4 + 98x^2 + 1	\( -\,2^{12}\cdot 13^{6}\cdot 1361^{6} \)	18T691	$[2, 20]$ (GRH)
18.14.511768170854128848340016746496.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 100x^14 + 196x^13 - 17x^12 - 340x^11 + 371x^10 + 70x^9 - 433x^8 + 250x^7 + 135x^6 - 204x^5 + 40x^4 + 53x^3 - 24x^2 - 4x + 1	\( 2^{12}\cdot 19^{6}\cdot 137^{6}\cdot 401669 \)	18T691	Trivial (GRH)
18.10.643576801371299298682142756864.1	x^18 - 9x^17 + 36x^16 - 84x^15 + 116x^14 - 56x^13 - 129x^12 + 332x^11 - 361x^10 + 144x^9 + 140x^8 - 242x^7 + 131x^6 + 18x^5 - 58x^4 + 21x^3 + 5x^2 - 5x - 1	\( 2^{12}\cdot 17\cdot 19^{6}\cdot 43\cdot 137^{6}\cdot 691 \)	18T691	Trivial (GRH)
18.18.11478406257373652556767037558784.1	x^18 - 9x^17 + 18x^16 + 60x^15 - 244x^14 - 56x^13 + 1103x^12 - 508x^11 - 2593x^10 + 1844x^9 + 3608x^8 - 2666x^7 - 3097x^6 + 1806x^5 + 1566x^4 - 471x^3 - 369x^2 + 7x + 13	\( 2^{12}\cdot 19^{6}\cdot 131\cdot 137^{6}\cdot 68771 \)	18T691	Trivial (GRH)
18.0.13584356571235485234285554696192.1	x^18 + 45x^16 + 746x^14 + 6151x^12 + 27975x^10 + 72137x^8 + 103555x^6 + 78272x^4 + 26852x^2 + 2603	\( -\,2^{24}\cdot 19^{7}\cdot 137^{7} \)	18T691	$[2, 174]$ (GRH)
18.10.54252214194223652651571312590848.1	x^18 - 4x^17 + 5x^16 + 74x^15 - 246x^14 - 658x^13 + 869x^12 - 8x^11 - 2565x^10 + 7242x^9 - 31697x^8 - 147104x^7 + 8809x^6 + 427280x^5 + 182280x^4 - 339974x^3 - 71912x^2 + 105228x - 16343	\( 2^{18}\cdot 19^{9}\cdot 97\cdot 137^{6} \)	18T691	$[2]$ (GRH)
18.14.10941166522253185418877915475775488.1	x^18 - 6x^17 - 22x^16 + 153x^15 + 111x^14 - 1403x^13 + 1519x^12 + 8546x^11 - 32778x^10 - 28605x^9 + 212813x^8 - 22535x^7 - 493999x^6 + 272376x^5 + 256459x^4 - 225999x^3 + 39522x^2 + 1448x - 8	\( 2^{12}\cdot 19^{6}\cdot 97^{5}\cdot 137^{6} \)	18T691	Trivial (GRH)
18.10.282514769958767480938292298837131264.1	x^18 - 6x^17 - 13x^16 + 108x^15 - 618x^14 - 1196x^13 + 11873x^12 + 42700x^11 + 149030x^10 + 238820x^9 - 1110397x^8 - 4980932x^7 - 6588732x^6 + 3658300x^5 + 27188867x^4 + 45731674x^3 + 39775891x^2 + 17641634x + 3073057	\( 2^{18}\cdot 17\cdot 19^{9}\cdot 43\cdot 137^{6}\cdot 691 \)	18T691	$[2]$ (GRH)
18.2.700234657424203866808186590449631232.1	x^18 - 7x^17 + 95x^16 - 591x^15 + 4105x^14 - 20513x^13 + 96803x^12 - 376616x^11 + 1269025x^10 - 3751483x^9 + 8345205x^8 - 16742719x^7 + 10955504x^6 + 17691872x^5 - 182729880x^4 + 495022927x^3 - 1015426051x^2 + 1597410665x - 1523530661	\( 2^{18}\cdot 19^{6}\cdot 97^{5}\cdot 137^{6} \)	18T691	$[2, 2]$ (GRH)
18.18.5038744865236856504759367079404765184.1	x^18 - 4x^17 - 130x^16 + 324x^15 + 6719x^14 - 8266x^13 - 171338x^12 + 55872x^11 + 2262507x^10 + 650658x^9 - 14829653x^8 - 9556120x^7 + 41552340x^6 + 28027896x^5 - 41210584x^4 - 12003724x^3 + 11749096x^2 - 1285426x + 19589	\( 2^{18}\cdot 19^{9}\cdot 131\cdot 137^{6}\cdot 68771 \)	18T691	$[2]$ (GRH)
18.2.95932148067115929752721562891599478784.1	x^18 - 2x^17 + 39x^16 + 326x^15 - 2249x^14 + 9080x^13 - 123356x^12 + 170874x^11 - 2261570x^10 + 6338506x^9 - 26302913x^8 + 55536852x^7 - 270486935x^6 + 110711082x^5 - 1270725859x^4 - 189474446x^3 - 2607092532x^2 - 253088998x - 4850760349	\( 2^{18}\cdot 19^{6}\cdot 97^{5}\cdot 137^{7} \)	18T691	$[2, 2, 2]$ (GRH)
18.6.252784711330137595917755359152316874752.1	x^18 - 7x^16 - 40x^15 - 2534x^14 - 7327x^13 - 63408x^12 - 133706x^11 + 234973x^10 + 334707x^9 + 17540223x^8 - 11745224x^7 + 129255659x^6 - 399346834x^5 + 162279935x^4 - 2344374796x^3 + 1466353619x^2 + 6558041127x - 7411396451	\( 2^{18}\cdot 19^{8}\cdot 97^{5}\cdot 137^{6} \)	18T691	$[2]$ (GRH)