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 64)

Label	Polynomial	Discriminant	Galois group	Class group
18.4.1835774562353817268224.1	x^18 - 6x^17 + 21x^16 - 47x^15 + 75x^14 - 81x^13 + 36x^12 + 45x^11 - 138x^10 + 169x^9 - 138x^8 + 45x^7 + 36x^6 - 81x^5 + 75x^4 - 47x^3 + 21x^2 - 6x + 1	\( -\,2^{12}\cdot 3^{24}\cdot 17^{4}\cdot 19 \)	18T839	Trivial
18.2.6568341307628680810496.2	x^18 - x^17 + x^16 + 2x^15 - 6x^14 + 9x^13 - 11x^12 - 10x^11 + 3x^10 - 30x^9 + 2x^8 - 34x^7 - 3x^6 - 13x^5 - 2x^4 - 5x^3 - 4x^2 - 2x - 1	\( 2^{12}\cdot 7^{12}\cdot 41^{5} \)	18T839	Trivial
18.4.6859999680374790844416.1	x^18 - 3x^17 + 6x^16 - 7x^15 - 3x^14 + 21x^13 - 36x^12 + 15x^11 + 39x^10 - 81x^9 + 63x^8 + 30x^7 - 89x^6 + 78x^5 + 6x^4 - 45x^3 + 30x^2 - 8	\( -\,2^{12}\cdot 3^{24}\cdot 17^{4}\cdot 71 \)	18T839	Trivial
18.4.10338309377466234089472.1	x^18 - 3x^16 - 6x^15 - 3x^13 - 6x^12 - 18x^11 - 6x^10 - x^9 + 27x^8 + 18x^7 + 23x^6 - 3x^5 - 3x^4 - 11x^3 - 6x^2 - 3x - 1	\( -\,2^{12}\cdot 3^{24}\cdot 17^{4}\cdot 107 \)	18T839	Trivial
18.2.105122248623208062517248.1	x^18 - 6x^17 + 21x^16 - 52x^15 + 93x^14 - 120x^13 + 84x^12 + 60x^11 - 249x^10 + 304x^9 - 123x^8 - 150x^7 + 230x^6 - 60x^5 - 102x^4 + 114x^3 - 81x^2 + 54x - 19	\( 2^{18}\cdot 3^{24}\cdot 17^{5} \)	18T839	Trivial
18.6.105122248623208062517248.1	x^18 - 6x^17 + 12x^16 + 6x^15 - 60x^14 + 42x^13 + 170x^12 - 312x^11 - 111x^10 + 758x^9 - 492x^8 - 528x^7 + 838x^6 - 276x^5 - 159x^4 + 168x^3 - 63x^2 + 12x - 1	\( 2^{18}\cdot 3^{24}\cdot 17^{5} \)	18T839	Trivial (GRH)
18.6.105122248623208062517248.2	x^18 - 3x^17 + 2x^15 - 3x^14 - 3x^13 - 9x^12 + 12x^10 + 28x^9 + 9x^8 + 6x^7 + x^6 - 15x^5 - 24x^4 - 16x^3 - 6x^2 + 1	\( 2^{18}\cdot 3^{24}\cdot 17^{5} \)	18T839	Trivial (GRH)
18.6.105122248623208062517248.3	x^18 - 12x^16 + 54x^14 - 103x^12 + 69x^10 + 33x^8 - 107x^6 + 72x^4 + 9x^2 - 17	\( 2^{18}\cdot 3^{24}\cdot 17^{5} \)	18T839	Trivial (GRH)
18.2.105410344139098495736057.1	x^18 - 6x^17 + 14x^16 - 11x^15 - x^14 - 38x^13 + 185x^12 - 355x^11 + 412x^10 - 329x^9 + 162x^8 + 46x^7 - 59x^6 - 62x^5 + 101x^4 - 29x^3 - 8x^2 + 7x - 1	\( 7^{12}\cdot 13^{5}\cdot 29^{5} \)	18T839	Trivial
18.6.105410344139098495736057.1	x^18 - x^17 - 6x^16 + 19x^15 - 28x^14 - 10x^13 + 117x^12 - 297x^11 + 458x^10 - 535x^9 + 458x^8 - 297x^7 + 117x^6 - 10x^5 - 28x^4 + 19x^3 - 6x^2 - x + 1	\( 7^{12}\cdot 13^{5}\cdot 29^{5} \)	18T839	Trivial
18.2.420373843688235571871744.1	x^18 + 3x^16 - 6x^15 + 10x^14 - 16x^13 - 40x^12 + 56x^11 - 71x^10 + 130x^9 + x^8 + 34x^7 + 81x^6 - 84x^5 - 2x^4 + 16x^3 + 24x^2 + 24x + 8	\( 2^{18}\cdot 7^{12}\cdot 41^{5} \)	18T839	Trivial
18.8.439039979543986614042624.1	x^18 - 6x^17 + 18x^16 - 20x^15 - 36x^14 + 162x^13 - 248x^12 + 150x^11 + 123x^10 - 452x^9 + 753x^8 - 864x^7 + 542x^6 + 54x^5 - 375x^4 + 256x^3 - 60x^2 + 1	\( -\,2^{18}\cdot 3^{24}\cdot 17^{4}\cdot 71 \)	18T839	Trivial (GRH)
18.8.2252941068516637518000128.1	x^18 - x^17 - 12x^16 + 8x^15 + 46x^14 - 16x^13 - 39x^12 - 9x^11 - 94x^10 + 48x^9 + 81x^8 - 17x^7 + 136x^6 - 88x^5 - 55x^4 + 91x^3 - 120x^2 - 16x + 64	\( -\,2^{12}\cdot 7^{15}\cdot 41^{5} \)	18T839	Trivial (GRH)
18.4.2838300712826617687965696.1	x^18 - 6x^17 + 18x^16 - 22x^15 - 24x^14 + 114x^13 - 70x^12 - 378x^11 + 885x^10 - 42x^9 - 3234x^8 + 7902x^7 - 11133x^6 + 10842x^5 - 7632x^4 + 3832x^3 - 1284x^2 + 240x - 8	\( -\,2^{18}\cdot 3^{27}\cdot 17^{5} \)	18T839	Trivial (GRH)
18.8.2838300712826617687965696.1	x^18 - 12x^16 - 16x^15 + 39x^14 + 102x^13 + 36x^12 - 72x^11 - 96x^10 + 78x^9 + 432x^8 + 648x^7 + 584x^6 + 372x^5 + 111x^4 - 32x^3 - 24x^2 + 1	\( -\,2^{18}\cdot 3^{27}\cdot 17^{5} \)	18T839	Trivial (GRH)
18.8.6727823911885316001103872.1	x^18 - 6x^16 + 29x^12 + 3x^10 - 63x^8 - 13x^6 + 114x^4 - 81x^2 + 17	\( -\,2^{24}\cdot 3^{24}\cdot 17^{5} \)	18T839	Trivial (GRH)
18.10.17814348159507645779393633.1	x^18 - 7x^17 + 7x^16 + 52x^15 - 116x^14 - 134x^13 + 557x^12 - 22x^11 - 1322x^10 + 911x^9 + 1487x^8 - 2052x^7 - 338x^6 + 1896x^5 - 718x^4 - 662x^3 + 506x^2 + 24x - 71	\( 7^{12}\cdot 13^{7}\cdot 29^{5} \)	18T839	Trivial (GRH)
18.6.17814348159507645779393633.1	x^18 - 9x^17 + 42x^16 - 121x^15 + 211x^14 - 140x^13 - 280x^12 + 886x^11 - 909x^10 - 249x^9 + 1338x^8 - 957x^7 - 259x^6 + 658x^5 - 200x^4 - 36x^3 + 76x^2 + 18x + 1	\( 7^{12}\cdot 13^{7}\cdot 29^{5} \)	18T839	Trivial (GRH)
18.4.26903925996047076599791616.1	x^18 + 5x^16 - 10x^14 - 11x^12 - 197x^10 + 169x^8 + 41x^6 + 230x^4 + 222x^2 + 41	\( -\,2^{24}\cdot 7^{12}\cdot 41^{5} \)	18T839	Trivial (GRH)
18.0.26903925996047076599791616.2	x^18 + 13x^16 + 50x^14 + 101x^12 + 339x^10 + 345x^8 + 629x^6 + 822x^4 + 346x^2 + 41	\( -\,2^{24}\cdot 7^{12}\cdot 41^{5} \)	18T839	$[2]$ (GRH)
18.10.26903925996047076599791616.1	x^18 - 13x^16 + 50x^14 - 101x^12 + 339x^10 - 345x^8 + 629x^6 - 822x^4 + 346x^2 - 41	\( 2^{24}\cdot 7^{12}\cdot 41^{5} \)	18T839	Trivial (GRH)
18.6.26903925996047076599791616.1	x^18 - 5x^16 - 10x^14 + 11x^12 - 197x^10 - 169x^8 + 41x^6 - 230x^4 + 222x^2 - 41	\( 2^{24}\cdot 7^{12}\cdot 41^{5} \)	18T839	Trivial (GRH)
18.0.27086248981307629272707072.1	x^18 - 9x^17 + 47x^16 - 172x^15 + 476x^14 - 1036x^13 + 1809x^12 - 2560x^11 + 2956x^10 - 2801x^9 + 2216x^8 - 1524x^7 + 963x^6 - 570x^5 + 288x^4 - 104x^3 + 28x^2 - 8x + 8	\( -\,2^{12}\cdot 7^{12}\cdot 83^{4}\cdot 10067 \)	18T839	Trivial (GRH)
18.4.73296257968169326435631104.1	x^18 + x^16 - 15x^14 - 27x^12 + 41x^10 + 144x^8 + 143x^6 + 70x^4 + 18x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 29^{4} \)	18T839	Trivial (GRH)
18.10.9165296128171039171583255533.1	x^18 - 6x^17 + 11x^16 - 6x^15 - 12x^14 + 77x^13 - 210x^12 + 375x^11 - 236x^10 - 122x^9 - 151x^8 - 641x^7 + 1177x^6 + 712x^5 - 538x^4 - 85x^3 + 85x^2 - 9x - 1	\( 7^{12}\cdot 13\cdot 83^{4}\cdot 181^{4} \)	18T839	Trivial (GRH)
18.6.9165296128171039171583255533.1	x^18 - 6x^17 + 11x^16 + x^15 - 149x^14 + 623x^13 - 980x^12 + 438x^11 + 1869x^10 - 5636x^9 + 4769x^8 + 2733x^7 - 5534x^6 + 939x^5 + 1039x^4 + 183x^3 - 385x^2 + 98x - 7	\( 7^{12}\cdot 13\cdot 83^{4}\cdot 181^{4} \)	18T839	Trivial (GRH)
18.6.10146939952861213092846003125.2	x^18 - 6x^17 + 30x^16 - 75x^15 + 71x^14 + 270x^13 - 1196x^12 + 2197x^11 - 2509x^10 + 3185x^9 - 5720x^8 + 5148x^7 + 3913x^6 - 11774x^5 + 7451x^4 + 1277x^3 - 3589x^2 + 1506x - 181	\( 5^{5}\cdot 13^{16}\cdot 47^{4} \)	18T839	Trivial (GRH)
18.10.28905933942693277387301036681.1	x^18 - 5x^17 - x^16 + 50x^15 - 57x^14 - 229x^13 + 468x^12 + 284x^11 - 1641x^10 + 1466x^9 + 1608x^8 - 4113x^7 + 1771x^6 + 1960x^5 - 2228x^4 + 496x^3 + 374x^2 - 246x + 41	\( 7^{12}\cdot 41\cdot 83^{4}\cdot 181^{4} \)	18T839	Trivial (GRH)
18.8.30315979500873437259852306763.1	x^18 - 3x^17 - 11x^16 + 40x^15 + 43x^14 - 245x^13 + 12x^12 + 860x^11 - 808x^10 - 1793x^9 + 3617x^8 + 2423x^7 - 7989x^6 - 3143x^5 + 8958x^4 + 4336x^3 - 3424x^2 - 2538x - 419	\( -\,7^{12}\cdot 43\cdot 83^{4}\cdot 181^{4} \)	18T839	Trivial (GRH)
18.8.30315979500873437259852306763.2	x^18 - 3x^17 + 7x^16 - 15x^15 - 17x^14 + 49x^13 - 123x^12 + 276x^11 - 282x^10 + 281x^9 + 1033x^8 + 89x^7 + 35x^6 + 1571x^5 + 1678x^4 + 272x^3 - 266x^2 - 70x + 7	\( -\,7^{12}\cdot 43\cdot 83^{4}\cdot 181^{4} \)	18T839	Trivial (GRH)
18.12.50056617315395675475570087911.1	x^18 - 7x^17 + 13x^16 - 3x^15 - 46x^14 + 180x^13 - 431x^12 + 1404x^11 - 1164x^10 - 118x^9 + 3235x^8 - 6255x^7 + 1271x^6 + 4693x^5 - 3082x^4 - 97x^3 + 539x^2 - 133x + 7	\( -\,7^{12}\cdot 71\cdot 83^{4}\cdot 181^{4} \)	18T839	Trivial (GRH)
18.4.50056617315395675475570087911.1	x^18 - 5x^17 - 3x^16 + 15x^15 + 22x^14 + 37x^13 + 214x^12 + 272x^11 + 262x^10 + 181x^9 + 54x^8 - 86x^7 - 402x^6 - 314x^5 + 282x^4 - 55x^3 + 51x^2 - 24x + 1	\( -\,7^{12}\cdot 71\cdot 83^{4}\cdot 181^{4} \)	18T839	$[2]$ (GRH)
18.4.58516890664476634710877708403.1	x^18 - 7x^17 + 2x^16 + 74x^15 - 164x^14 + 5x^13 + 191x^12 + 227x^11 - 698x^10 + 280x^9 + 396x^8 - 621x^7 + 295x^6 + 146x^5 + 197x^4 - 370x^3 - 15x^2 + 39x + 71	\( -\,7^{12}\cdot 83^{5}\cdot 181^{4} \)	18T839	$[4]$ (GRH)
18.12.64157072897197274201082788731.1	x^18 - x^17 - 18x^16 + 41x^15 + 63x^14 - 293x^13 + 120x^12 + 718x^11 - 787x^10 - 855x^9 + 1199x^8 + 1387x^7 - 1952x^6 - 1291x^5 + 2674x^4 - 946x^3 - 79x^2 + 19x + 1	\( -\,7^{13}\cdot 13\cdot 83^{4}\cdot 181^{4} \)	18T839	Trivial (GRH)
18.8.64157072897197274201082788731.1	x^18 - 8x^17 + 18x^16 + 28x^15 - 172x^14 + 172x^13 - 636x^12 + 4572x^11 - 8806x^10 + 759x^9 + 8757x^8 - 3376x^7 + 22032x^6 - 58527x^5 + 44608x^4 - 17877x^3 + 17046x^2 - 8507x - 181	\( -\,7^{13}\cdot 13\cdot 83^{4}\cdot 181^{4} \)	18T839	Trivial (GRH)
18.8.64157072897197274201082788731.2	x^18 - x^17 - 16x^16 + 2x^15 - 4x^14 - 224x^13 - 279x^12 - 539x^11 - 1702x^10 - 2042x^9 - 2615x^8 - 2215x^7 + 2318x^6 + 3409x^5 + 2898x^4 + 2065x^3 - 3521x^2 - 2191x + 1267	\( -\,7^{13}\cdot 13\cdot 83^{4}\cdot 181^{4} \)	18T839	Trivial (GRH)
18.10.68387209571737753818736598977.1	x^18 - 6x^17 + 7x^16 - x^15 - 40x^14 + 448x^13 - 819x^12 + 445x^11 + 2x^10 - 5122x^9 + 4397x^8 + 988x^7 + 1095x^6 + 21162x^5 + 11423x^4 + 6924x^3 + 12122x^2 + 3092x - 461	\( 7^{12}\cdot 83^{4}\cdot 97\cdot 181^{4} \)	18T839	Trivial (GRH)
18.12.117738804108043349358031051847.1	x^18 - 9x^17 + 38x^16 - 100x^15 + 136x^14 + 84x^13 - 707x^12 + 1252x^11 - 825x^10 - 726x^9 + 2073x^8 - 1786x^7 + 402x^6 + 481x^5 - 435x^4 + 126x^3 + 3x^2 - 8x + 1	\( -\,7^{12}\cdot 83^{4}\cdot 167\cdot 181^{4} \)	18T839	Trivial (GRH)
18.8.117738804108043349358031051847.1	x^18 - 3x^17 - 9x^16 + 32x^15 + 5x^14 - 76x^13 + 224x^12 - 696x^11 - 1115x^10 + 6107x^9 + 3031x^8 - 21571x^7 - 7369x^6 + 40346x^5 + 15037x^4 - 38827x^3 - 17799x^2 + 14982x + 8287	\( -\,7^{12}\cdot 83^{4}\cdot 167\cdot 181^{4} \)	18T839	Trivial (GRH)
18.2.138889487480745747446300103077.1	x^18 - 9x^17 + 61x^16 - 284x^15 + 1050x^14 - 3094x^13 + 7337x^12 - 14070x^11 + 20759x^10 - 22010x^9 + 9718x^8 + 17172x^7 - 51325x^6 + 73982x^5 - 73160x^4 + 51155x^3 - 24349x^2 + 7066x - 923	\( 7^{12}\cdot 83^{4}\cdot 181^{4}\cdot 197 \)	18T839	Trivial (GRH)
18.14.253673498821530327321150078125.1	x^18 - x^17 - 38x^16 + 89x^15 + 462x^14 - 1812x^13 - 997x^12 + 12967x^11 - 12702x^10 - 33968x^9 + 80789x^8 - 16580x^7 - 124391x^6 + 155097x^5 - 42002x^4 - 51257x^3 + 48302x^2 - 15785x + 1825	\( 5^{7}\cdot 13^{16}\cdot 47^{4} \)	18T839	Trivial (GRH)
18.14.409618234651336442976143958821.1	x^18 - 2x^17 - 27x^16 + 57x^15 + 211x^14 - 400x^13 - 784x^12 + 1078x^11 + 1630x^10 - 615x^9 - 1592x^8 - 1711x^7 + 46x^6 + 2054x^5 + 420x^4 - 526x^3 - 50x^2 + 12x + 1	\( 7^{13}\cdot 83^{5}\cdot 181^{4} \)	18T839	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)
18.16.33998313476060924767019948582143.1	x^18 - 4x^17 - 36x^16 + 118x^15 + 552x^14 - 1126x^13 - 4873x^12 + 2699x^11 + 22549x^10 + 16738x^9 - 21488x^8 - 33368x^7 - 4380x^6 + 13795x^5 + 6374x^4 - 1079x^3 - 981x^2 - 13x + 41	\( -\,7^{13}\cdot 83^{6}\cdot 181^{4} \)	18T839	Trivial (GRH)
18.10.74140900471891896178682056546601.1	x^18 - 39x^16 - 46x^15 + 612x^14 + 1445x^13 - 4468x^12 - 17664x^11 + 10205x^10 + 107520x^9 + 54703x^8 - 348932x^7 - 406768x^6 + 589667x^5 + 1030277x^4 - 440590x^3 - 1191588x^2 + 68763x + 511909	\( 7^{13}\cdot 83^{5}\cdot 181^{5} \)	18T839	Trivial (GRH)
18.2.74140900471891896178682056546601.1	x^18 - x^17 + 6x^16 + 74x^15 - 324x^14 + 1711x^13 - 5870x^12 + 19528x^11 - 48163x^10 + 113360x^9 - 225634x^8 + 385625x^7 - 551651x^6 + 647554x^5 - 689064x^4 + 582461x^3 - 427833x^2 + 196056x - 79183	\( 7^{13}\cdot 83^{5}\cdot 181^{5} \)	18T839	$[2, 4]$ (GRH)
18.6.74140900471891896178682056546601.1	x^18 - 5x^17 - x^16 + 50x^15 - 235x^14 + 376x^13 + 800x^12 - 2690x^11 + 7410x^10 - 14085x^9 - 3864x^8 + 63304x^7 - 160451x^6 + 115392x^5 + 156071x^4 - 753228x^3 + 1135381x^2 - 853458x + 403481	\( 7^{13}\cdot 83^{5}\cdot 181^{5} \)	18T839	$[2]$ (GRH)
18.12.518986303303243273250774395826207.1	x^18 - 7x^16 - 15x^15 - 188x^14 - 1277x^13 - 3341x^12 + 15250x^11 + 85568x^10 + 144577x^9 - 22645x^8 - 636218x^7 - 453143x^6 + 716395x^5 + 616323x^4 - 171844x^3 - 222992x^2 - 49210x - 3031	\( -\,7^{14}\cdot 83^{5}\cdot 181^{5} \)	18T839	Trivial (GRH)
18.12.531991885400569969002204528640000.1	x^18 + 3x^16 - 74x^14 - 59x^12 + 1459x^10 - 2534x^8 + 526x^6 + 376x^4 - 64x^2 + 1	\( -\,2^{18}\cdot 5^{4}\cdot 13^{16}\cdot 47^{4} \)	18T839	Trivial (GRH)
18.12.692461388235031982051012051474503.1	x^18 - 9x^17 + 30x^16 - 36x^15 - 50x^14 + 266x^13 - 427x^12 + 118x^11 + 719x^10 - 1340x^9 + 882x^8 + 480x^7 - 1281x^6 + 742x^5 + 7x^4 - 131x^3 + 17x^2 + 12x + 1	\( -\,7^{12}\cdot 83^{4}\cdot 181^{4}\cdot 982183 \)	18T839	Trivial (GRH)