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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 56)

Label	Polynomial	Discriminant	Galois group	Class group
18.6.870649295878306573433.2	x^18 - 7x^16 - 6x^15 + 19x^14 + 30x^13 - 11x^12 - 55x^11 - 37x^10 + 44x^9 + 80x^8 - 23x^7 - 96x^6 + 10x^5 + 72x^4 + 2x^3 - 22x^2 - 3x + 1	\( 7^{12}\cdot 41^{3}\cdot 97^{3} \)	18T840	Trivial (GRH)
18.6.870649295878306573433.3	x^18 - x^17 - 2x^16 - 4x^15 + x^14 + 20x^13 + 11x^12 - 42x^11 - 37x^10 + 53x^9 + 64x^8 - 35x^7 - 62x^6 + 7x^5 + 32x^4 + 2x^3 - 9x^2 - x + 1	\( 7^{12}\cdot 41^{3}\cdot 97^{3} \)	18T840	Trivial (GRH)
18.6.870649295878306573433.4	x^18 - 3x^17 + 3x^16 - 5x^15 + 2x^14 + 29x^13 - 51x^12 + 18x^11 + 32x^10 - 79x^9 + 86x^8 + 23x^7 - 121x^6 + 40x^5 + 67x^4 - 37x^3 - 17x^2 + 14x - 1	\( 7^{12}\cdot 41^{3}\cdot 97^{3} \)	18T840	Trivial (GRH)
18.4.356593228716323827483591.1	x^18 - 3x^17 + x^16 + 3x^15 - 11x^14 - 5x^13 + 91x^12 - 83x^11 - 96x^10 + 424x^9 - 754x^8 + 119x^7 + 931x^6 - 1026x^5 + 635x^4 + 588x^3 - 1401x^2 - 116x + 841	\( -\,7^{12}\cdot 97^{2}\cdot 1399^{3} \)	18T840	Trivial (GRH)
18.6.8191939224918986549431097.1	x^18 - 4x^17 + 8x^16 - 18x^15 - 15x^14 + 165x^13 - 382x^12 + 684x^11 - 772x^10 - 256x^9 + 2164x^8 - 3244x^7 + 3710x^6 + 716x^5 - 2241x^4 + 4565x^3 - 3901x^2 - 1600x + 1709	\( 7^{12}\cdot 41^{3}\cdot 97^{5} \)	18T840	Trivial (GRH)
18.2.8191939224918986549431097.2	x^18 - 4x^17 + 8x^16 - 16x^15 + 35x^14 - 62x^13 + 27x^12 - 68x^11 + 80x^10 + 46x^9 - 286x^8 - 300x^7 + 127x^6 + 130x^5 + 619x^4 - 1768x^3 - 155x^2 - 1450x + 125	\( 7^{12}\cdot 41^{3}\cdot 97^{5} \)	18T840	$[2]$ (GRH)
18.4.9935038298290147032825856.3	x^18 + 6x^16 - 14x^14 - 172x^12 - 283x^10 + 806x^8 + 3593x^6 + 5423x^4 + 4068x^2 + 1399	\( -\,2^{18}\cdot 7^{12}\cdot 1399^{3} \)	18T840	Trivial (GRH)
18.2.21106009685505727678262841.1	x^18 + 3x^16 - 11x^15 - 6x^14 - 63x^13 - 27x^12 - 24x^11 - 237x^10 - 98x^9 - 120x^8 + 156x^7 + 461x^6 + 561x^5 - 588x^4 - 300x^3 + 237x^2 - 189x - 269	\( 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.2.21106009685505727678262841.2	x^18 - 3x^17 + 12x^16 - 4x^15 + 9x^14 + 93x^13 + 11x^12 + 174x^11 + 417x^10 + 290x^9 + 732x^8 + 1017x^7 + 667x^6 + 909x^5 + 732x^4 + 128x^3 + 99x^2 - 246x - 269	\( 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.6.21106009685505727678262841.3	x^18 - 3x^17 + 8x^15 - 33x^14 + 33x^13 + 103x^12 - 162x^11 - 468x^10 - 121x^9 + 882x^8 + 1833x^7 + 2375x^6 + 1665x^5 - 66x^4 - 1117x^3 - 708x^2 - 102x + 19	\( 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.10.21106009685505727678262841.5	x^18 - 9x^17 + 42x^16 - 120x^15 + 207x^14 - 171x^13 - 106x^12 + 528x^11 - 840x^10 + 900x^9 - 684x^8 + 54x^7 + 950x^6 - 1500x^5 + 1074x^4 - 378x^3 + 51x^2 + 3x - 1	\( 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.10.21106009685505727678262841.6	x^18 - 15x^16 - 8x^15 + 57x^14 + 51x^13 - 3x^12 + 33x^11 - 84x^10 - 198x^9 - 246x^8 - 219x^7 + 25x^6 - 51x^5 - 27x^4 + 60x^3 + 3x^2 - 9x + 1	\( 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.10.21106009685505727678262841.7	x^18 - 3x^17 - 6x^16 + 31x^15 - 36x^14 - 33x^13 + 169x^12 - 243x^11 - 18x^10 + 894x^9 - 822x^8 - 879x^7 + 1772x^6 + 168x^5 - 1302x^4 + 109x^3 + 288x^2 - 18x - 19	\( 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.10.21106009685505727678262841.8	x^18 - 9x^17 + 30x^16 - 36x^15 - 63x^14 + 357x^13 - 712x^12 + 645x^11 + 267x^10 - 1742x^9 + 2715x^8 - 2361x^7 + 1121x^6 - 102x^5 - 195x^4 + 96x^3 - 6x^2 - 6x + 1	\( 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.10.161536237646646866899894272.1	x^18 - 3x^16 - 30x^14 + 73x^12 + 330x^10 - 630x^8 - 1427x^6 + 1839x^4 + 2205x^2 - 1297	\( 2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T840	Trivial (GRH)
18.10.161536237646646866899894272.2	x^18 - 15x^16 + 102x^14 - 477x^12 + 1344x^10 - 2538x^8 + 4907x^6 - 7833x^4 + 5985x^2 - 1297	\( 2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T840	Trivial (GRH)
18.2.161536237646646866899894272.3	x^18 + 6x^16 - 3x^14 - 30x^12 - 156x^10 - 1668x^8 - 4992x^6 - 5601x^4 - 3243x^2 - 1297	\( 2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T840	Trivial (GRH)
18.6.161536237646646866899894272.3	x^18 - 6x^16 + 15x^14 - 102x^12 + 87x^10 - 342x^8 + 584x^6 + 3168x^4 - 3315x^2 - 1297	\( 2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T840	Trivial (GRH)
18.2.161536237646646866899894272.4	x^18 + 24x^16 + 228x^14 + 1119x^12 + 3075x^10 + 4812x^8 + 4358x^6 + 2451x^4 + 186x^2 - 1297	\( 2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T840	Trivial (GRH)
18.6.161536237646646866899894272.4	x^18 - 3x^16 - 9x^14 - 65x^12 - 21x^10 - 576x^8 - 2081x^6 + 5388x^4 + 696x^2 - 1297	\( 2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T840	Trivial (GRH)
18.2.161536237646646866899894272.5	x^18 + 18x^16 + 90x^14 + 73x^12 - 75x^10 - 219x^8 - 1112x^6 - 1275x^4 - 903x^2 - 1297	\( 2^{18}\cdot 3^{24}\cdot 1297^{3} \)	18T840	Trivial (GRH)
18.8.1519118496790264747045229351.2	x^18 - 7x^17 + 9x^16 + 8x^15 + 32x^14 - 2x^13 - 107x^12 - 220x^11 - 1266x^10 - 424x^9 + 3265x^8 + 10160x^7 + 7835x^6 - 11138x^5 - 22674x^4 - 15768x^3 + 10383x^2 + 11217x - 5333	\( -\,7^{12}\cdot 97^{2}\cdot 22679^{3} \)	18T840	$[2]$ (GRH)
18.8.1519118496790264747045229351.3	x^18 - 4x^17 - 16x^16 + 82x^15 + 65x^14 - 642x^13 - 18x^12 + 3076x^11 - 561x^10 - 11479x^9 + 4023x^8 + 30868x^7 - 12276x^6 - 62804x^5 + 29206x^4 + 80746x^3 - 39498x^2 - 42537x + 559	\( -\,7^{12}\cdot 97^{2}\cdot 22679^{3} \)	18T840	$[2]$ (GRH)
18.0.93478775348611993431858479104.1	x^18 + 11x^16 + 51x^14 + 745x^12 - 140x^10 + 19094x^8 + 269471x^6 + 1026867x^4 + 5987616x^2 + 13163191	\( -\,2^{18}\cdot 7^{12}\cdot 97^{2}\cdot 1399^{3} \)	18T840	$[2]$ (GRH)
18.0.93478775348611993431858479104.2	x^18 - 8x^16 + 53x^14 + 1945x^12 - 7446x^10 + 57923x^8 + 1009829x^6 - 868778x^4 - 504303x^2 + 13163191	\( -\,2^{18}\cdot 7^{12}\cdot 97^{2}\cdot 1399^{3} \)	18T840	$[2]$ (GRH)
18.14.112473925614060022797462679689.4	x^18 - 3x^17 - 21x^16 + 74x^15 + 21x^14 - 30x^13 - 230x^12 - 2337x^11 + 6297x^10 + 332x^9 - 12261x^8 + 15162x^7 - 8515x^6 - 23616x^5 + 38559x^4 + 12791x^3 - 32574x^2 - 2310x + 8713	\( 3^{24}\cdot 73^{5}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.6.112473925614060022797462679689.4	x^18 - 3x^17 + 15x^16 - 76x^15 + 114x^14 - 552x^13 + 1212x^12 - 429x^11 + 6294x^10 + 3507x^9 - 8640x^8 - 49698x^7 - 144749x^6 + 49869x^5 + 190836x^4 + 572016x^3 + 2343x^2 - 55662x + 38699	\( 3^{24}\cdot 73^{5}\cdot 577^{3} \)	18T840	$[2]$ (GRH)
18.14.112473925614060022797462679689.5	x^18 - 3x^17 - 9x^16 - 21x^15 + 60x^14 + 495x^13 + 229x^12 - 1530x^11 - 8130x^10 + 1038x^9 + 46149x^8 - 18165x^7 - 83834x^6 + 67371x^5 + 15687x^4 - 25470x^3 + 6123x^2 - 549x + 17	\( 3^{24}\cdot 73^{5}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.0.536495523810946581168977084416.2	x^18 + 42x^16 + 712x^14 + 6340x^12 + 32570x^10 + 100735x^8 + 191478x^6 + 225333x^4 + 158637x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.0.536495523810946581168977084416.3	x^18 + 38x^16 + 492x^14 + 1997x^12 - 5968x^10 - 49743x^8 + 191x^6 + 250734x^4 + 229788x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.4.536495523810946581168977084416.3	x^18 - 15x^16 - 15x^14 + 1229x^12 + 1279x^10 - 20150x^8 - 33574x^6 + 67612x^4 + 145163x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.12.536495523810946581168977084416.4	x^18 - 29x^16 + 266x^14 - 686x^12 - 3998x^10 + 35265x^8 - 113818x^6 + 188896x^4 - 158637x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.4.536495523810946581168977084416.4	x^18 + 19x^16 + 53x^14 - 831x^12 - 5112x^10 + 264x^8 + 72193x^6 + 214904x^4 + 228121x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.12.536495523810946581168977084416.5	x^18 - x^16 - 153x^14 + 243x^12 + 7690x^10 - 20566x^8 - 99951x^6 + 388894x^4 - 362889x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.4.536495523810946581168977084416.5	x^18 - x^16 + 46x^14 + 1941x^12 + 10885x^10 + 4523x^8 - 75525x^6 - 101223x^4 + 28425x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.8.536495523810946581168977084416.5	x^18 - 4x^16 - 69x^14 - 691x^12 + 833x^10 + 17005x^8 - 9970x^6 - 103479x^4 + 97898x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.12.536495523810946581168977084416.6	x^18 - 34x^16 + 489x^14 - 3705x^12 + 14844x^10 - 24951x^8 - 16284x^6 + 116304x^4 - 139614x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.4.536495523810946581168977084416.6	x^18 - 136x^14 - 849x^12 - 1943x^10 - 5743x^8 - 23697x^6 - 31775x^4 + 24746x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.8.536495523810946581168977084416.6	x^18 + 12x^16 - 124x^14 - 697x^12 + 799x^10 - 5991x^8 + 36251x^6 + 4835x^4 - 105758x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.12.536495523810946581168977084416.7	x^18 - 46x^16 + 842x^14 - 7768x^12 + 37404x^10 - 82300x^8 + 11622x^6 + 244658x^4 - 293189x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.4.536495523810946581168977084416.7	x^18 + 4x^16 - 146x^14 - 257x^12 + 8399x^10 + 10751x^8 - 155141x^6 - 435617x^4 - 250132x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.8.536495523810946581168977084416.7	x^18 + 6x^16 - 273x^14 + 1561x^12 + 1861x^10 - 33307x^8 + 57262x^6 + 69091x^4 - 188968x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.4.536495523810946581168977084416.8	x^18 + 6x^16 - 141x^14 - 1131x^12 - 1553x^10 - 3049x^8 + 7665x^6 + 79790x^4 + 129334x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.8.536495523810946581168977084416.8	x^18 + 11x^16 + 19x^14 - 303x^12 - 2742x^10 - 2442x^8 + 46471x^6 + 44390x^4 - 186765x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.8.536495523810946581168977084416.9	x^18 - 27x^16 + 220x^14 - 401x^12 - 3487x^10 + 16708x^8 + 2846x^6 - 83820x^4 - 29908x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.8.536495523810946581168977084416.10	x^18 + x^16 - 122x^14 + 268x^12 + 2966x^10 - 10497x^8 - 8225x^6 + 79499x^4 - 120593x^2 + 52879	\( -\,2^{18}\cdot 7^{12}\cdot 52879^{3} \)	18T840	Trivial (GRH)
18.10.5532813802997213476490534191104.1	x^18 - 9x^16 - 138x^14 + 721x^12 + 6387x^10 - 11676x^8 - 63255x^6 + 118605x^4 + 13194x^2 - 42121	\( 2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.6.5532813802997213476490534191104.1	x^18 + 30x^16 + 165x^14 - 2146x^12 - 22428x^10 - 32517x^8 + 157007x^6 + 354468x^4 - 1338x^2 - 42121	\( 2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.10.5532813802997213476490534191104.2	x^18 - 18x^16 + 30x^14 + 1050x^12 - 5733x^10 + 48x^8 + 34436x^6 + 3438x^4 - 66138x^2 - 42121	\( 2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T840	Trivial (GRH)
18.14.5532813802997213476490534191104.2	x^18 - 45x^16 + 666x^14 - 3458x^12 - 585x^10 + 47706x^8 - 75542x^6 - 56694x^4 + 126741x^2 - 42121	\( 2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{3} \)	18T840	Trivial (GRH)