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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.10.55412477560287811237001.1	x^18 - 6x^17 + 13x^16 - 12x^15 - 8x^14 + 56x^13 - 92x^12 + 64x^11 - 25x^10 + 24x^9 + 81x^8 - 221x^7 + 116x^6 - 31x^5 + 102x^4 - 54x^3 - 14x^2 + 6x + 1	\( 7^{12}\cdot 13^{4}\cdot 41\cdot 43^{4} \)	18T696	Trivial (GRH)
18.8.58115525246155509346123.1	x^18 - 4x^17 + 6x^16 + 5x^15 - 35x^14 + 77x^13 - 114x^12 + 119x^11 - 52x^10 - 90x^9 + 173x^8 - 163x^7 + 142x^6 - 187x^5 + 147x^4 + 13x^3 - 50x^2 + 14x - 1	\( -\,7^{12}\cdot 13^{4}\cdot 43^{5} \)	18T696	Trivial (GRH)
18.12.95958192848303282873831.1	x^18 - 3x^17 - 7x^16 + 34x^15 - 34x^14 - 21x^13 + 134x^12 - 245x^11 + 115x^10 + 105x^9 - 10x^8 - 106x^7 + 17x^6 + 82x^5 - 131x^4 + 66x^3 + 14x^2 - 11x - 1	\( -\,7^{12}\cdot 13^{4}\cdot 43^{4}\cdot 71 \)	18T696	Trivial (GRH)
18.4.112176478963509471528563.1	x^18 - 4x^17 + 7x^16 - 10x^15 + 8x^14 - 2x^13 - 8x^12 + 20x^11 - 29x^10 + 33x^9 - 29x^8 + 20x^7 - 8x^6 - 2x^5 + 8x^4 - 10x^3 + 7x^2 - 4x + 1	\( -\,7^{12}\cdot 13^{4}\cdot 43^{4}\cdot 83 \)	18T696	Trivial (GRH)
18.8.171643528052598829929247.1	x^18 - 5x^17 - x^16 + 46x^15 - 73x^14 - 72x^13 + 294x^12 - 197x^11 - 206x^10 + 343x^9 - 52x^8 - 160x^7 + 82x^6 + 3x^5 - 4x^4 - x^3 + 2x^2 + 2x - 1	\( -\,7^{12}\cdot 13^{4}\cdot 43^{4}\cdot 127 \)	18T696	Trivial (GRH)
18.10.266250197057968263748517.1	x^18 - 3x^17 - 2x^16 + 9x^15 - 10x^14 - 14x^13 + 20x^12 + 46x^11 + 21x^10 - 78x^9 - 32x^8 + 42x^7 - 33x^6 + 4x^5 + 53x^4 - 3x^3 - 19x^2 - 2x + 1	\( 7^{12}\cdot 13^{4}\cdot 43^{4}\cdot 197 \)	18T696	Trivial (GRH)
18.12.755501828200021621499599.2	x^18 - 3x^17 - 4x^16 + 26x^15 - 38x^14 + 14x^13 + 29x^12 - 84x^11 + 246x^10 - 483x^9 + 496x^8 - 218x^7 - 122x^6 + 284x^5 - 162x^4 - 2x^3 + 24x^2 - 2x - 1	\( -\,7^{12}\cdot 13^{5}\cdot 43^{5} \)	18T696	Trivial (GRH)
18.6.3722272632023871684687649.1	x^18 - 2x^17 - 2x^16 + 6x^15 - 5x^14 - 27x^13 + 5x^12 + 8x^11 - 12x^10 + 133x^9 + 314x^8 + 619x^7 + 1242x^6 + 1662x^5 + 1442x^4 + 860x^3 + 343x^2 + 77x + 7	\( 7^{12}\cdot 769^{5} \)	18T696	Trivial (GRH)
18.6.8504594297094853771126397.1	x^18 - 9x^17 + 37x^16 - 92x^15 + 144x^14 - 112x^13 - 70x^12 + 342x^11 - 503x^10 + 381x^9 - 43x^8 - 250x^7 + 302x^6 - 164x^5 + 18x^4 + 36x^3 - 26x^2 + 8x - 1	\( 7^{13}\cdot 251\cdot 769^{4} \)	18T696	Trivial (GRH)
18.12.26055908424167101792813543.1	x^18 - 5x^17 + 8x^16 - 13x^15 + 18x^14 + 21x^13 + 12x^12 - 88x^11 - 179x^10 + 150x^9 - 7x^8 + 1027x^7 - 596x^6 - 1311x^5 + 621x^4 + 524x^3 - 133x^2 - 56x + 7	\( -\,7^{13}\cdot 769^{5} \)	18T696	Trivial (GRH)
18.4.26055908424167101792813543.1	x^18 - 5x^17 + 13x^16 + 7x^15 - 106x^14 + 325x^13 - 549x^12 + 787x^11 - 816x^10 + 680x^9 - 793x^8 + 726x^7 - 294x^6 + 25x^5 - 28x^4 + 62x^3 - 21x^2 - 14x + 7	\( -\,7^{13}\cdot 769^{5} \)	18T696	Trivial (GRH)
18.14.182391358969169712549694801.1	x^18 - 2x^17 - 10x^16 + 30x^15 - 41x^14 + 7x^13 + 125x^12 - 552x^11 + 755x^10 + 2717x^9 - 562x^8 - 2908x^7 - 85x^6 + 1169x^5 + 130x^4 - 173x^3 - 27x^2 + 6x + 1	\( 7^{14}\cdot 769^{5} \)	18T696	Trivial (GRH)
18.6.182391358969169712549694801.1	x^18 - 6x^17 + 14x^16 - 3x^15 - 114x^14 + 508x^13 - 1393x^12 + 2851x^11 - 4515x^10 + 5727x^9 - 5593x^8 + 4295x^7 - 2149x^6 + 338x^5 + 290x^4 - 248x^3 + 98x^2 - 19x + 1	\( 7^{14}\cdot 769^{5} \)	18T696	Trivial (GRH)
18.6.259137127072607416174362457.1	x^18 - 6x^17 + 10x^16 + 6x^15 - 8x^14 - 126x^13 + 172x^12 + 506x^11 - 1502x^10 + 1040x^9 + 1517x^8 - 2770x^7 + 3257x^6 - 1144x^5 - 482x^4 + 1698x^3 - 977x^2 + 320x - 41	\( 7^{15}\cdot 13^{5}\cdot 43^{5} \)	18T696	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)
18.8.354293866282050926558838784.1	x^18 + 6x^16 - 19x^14 - 176x^12 - 249x^10 + 138x^8 + 158x^6 - 47x^4 - 10x^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)
18.8.354293866282050926558838784.2	x^18 - 4x^16 - 24x^14 + 48x^12 + 222x^10 + 115x^8 - 206x^6 - 230x^4 - 62x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.12.657670877484675513225221791.1	x^18 - 9x^17 + 28x^16 - 20x^15 - 80x^14 + 196x^13 - 98x^12 - 218x^11 + 379x^10 - 135x^9 - 222x^8 + 262x^7 - 46x^6 - 86x^5 + 52x^4 + 6x^3 - 11x^2 + x + 1	\( -\,7^{12}\cdot 83\cdot 769^{4}\cdot 1637 \)	18T696	Trivial (GRH)
18.2.1127975196022958661050983009.1	x^18 - 9x^17 + 52x^16 - 212x^15 + 678x^14 - 1750x^13 + 3742x^12 - 6696x^11 + 10081x^10 - 12763x^9 + 13490x^8 - 11752x^7 + 8214x^6 - 4400x^5 + 1614x^4 - 266x^3 - 87x^2 + 63x - 13	\( 7^{12}\cdot 41\cdot 673^{4}\cdot 9689 \)	18T696	$[3]$ (GRH)
18.0.2152830165694741754368725851.1	x^18 - 9x^17 + 59x^16 - 268x^15 + 996x^14 - 2996x^13 + 7680x^12 - 16674x^11 + 31325x^10 - 50541x^9 + 70611x^8 - 84430x^7 + 86276x^6 - 73836x^5 + 52138x^4 - 29154x^3 + 12258x^2 - 3436x + 463	\( -\,7^{12}\cdot 13^{4}\cdot 41\cdot 43^{4}\cdot 38851 \)	18T696	$[32]$ (GRH)
18.14.2155819509191297536643900133.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 108x^14 + 252x^13 - 129x^12 - 396x^11 + 783x^10 - 142x^9 - 945x^8 + 666x^7 + 444x^6 - 459x^5 - 81x^4 + 108x^3 + 9x^2 - 9x - 1	\( 3^{36}\cdot 19^{4}\cdot 307\cdot 359 \)	18T696	Trivial (GRH)
18.4.4605820261666662045264904192.1	x^18 + 17x^16 + 101x^14 + 220x^12 - 66x^10 - 936x^8 - 1254x^6 - 533x^4 + 13	\( -\,2^{18}\cdot 7^{12}\cdot 13^{5}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.8.4605820261666662045264904192.1	x^18 + 2x^16 - 16x^14 - 41x^12 + 51x^10 + 210x^8 + 123x^6 - 65x^4 - 39x^2 + 13	\( -\,2^{18}\cdot 7^{12}\cdot 13^{5}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.4.4605820261666662045264904192.2	x^18 + x^16 - 36x^14 - 85x^12 + 203x^10 + 921x^8 + 1203x^6 + 689x^4 + 169x^2 + 13	\( -\,2^{18}\cdot 7^{12}\cdot 13^{5}\cdot 43^{4} \)	18T696	$[2]$ (GRH)
18.8.4605820261666662045264904192.2	x^18 - 35x^14 + 2x^12 + 357x^10 - 35x^8 - 981x^6 + 455x^4 + 182x^2 + 13	\( -\,2^{18}\cdot 7^{12}\cdot 13^{5}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.10.4605820261666662045264904192.1	x^18 - 8x^16 - 13x^14 + 81x^12 + 70x^10 - 251x^8 - 162x^6 + 234x^4 + 104x^2 - 13	\( 2^{18}\cdot 7^{12}\cdot 13^{5}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.14.4605820261666662045264904192.1	x^18 - 17x^16 + 101x^14 - 220x^12 - 66x^10 + 936x^8 - 1254x^6 + 533x^4 - 13	\( 2^{18}\cdot 7^{12}\cdot 13^{5}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.10.4605820261666662045264904192.2	x^18 + 9x^16 - 15x^14 - 199x^12 + 23x^10 + 836x^8 - 771x^6 - 52x^4 + 182x^2 - 13	\( 2^{18}\cdot 7^{12}\cdot 13^{5}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.14.4605820261666662045264904192.2	x^18 - 17x^16 + 88x^14 - 145x^12 - 81x^10 + 421x^8 - 318x^6 + 65x^2 - 13	\( 2^{18}\cdot 7^{12}\cdot 13^{5}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.10.4605820261666662045264904192.3	x^18 - 12x^16 + 9x^14 + 169x^12 + 32x^10 - 335x^8 - 19x^6 + 156x^4 + 13x^2 - 13	\( 2^{18}\cdot 7^{12}\cdot 13^{5}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.10.4605820261666662045264904192.4	x^18 + 9x^16 + x^14 - 131x^12 - 114x^10 + 359x^8 + 123x^6 - 364x^4 + 130x^2 - 13	\( 2^{18}\cdot 7^{12}\cdot 13^{5}\cdot 43^{4} \)	18T696	Trivial (GRH)
18.12.8882184730747543215052423168.1	x^18 - 7x^16 - 27x^14 + 245x^12 - 163x^10 - 1078x^8 + 2036x^6 - 1232x^4 + 217x^2 + 7	\( -\,2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T696	Trivial (GRH)
18.12.8882184730747543215052423168.2	x^18 - 14x^16 + 50x^14 + 49x^12 - 471x^10 + 252x^8 + 1049x^6 - 812x^4 - 350x^2 + 7	\( -\,2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T696	Trivial (GRH)
18.2.8882184730747543215052423168.1	x^18 + 22x^16 + 192x^14 + 847x^12 + 1965x^10 + 2109x^8 + 99x^6 - 1855x^4 - 1470x^2 - 343	\( 2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T696	$[2]$ (GRH)
18.6.8882184730747543215052423168.3	x^18 + 7x^16 - 12x^14 - 154x^12 - 120x^10 + 658x^8 + 748x^6 - 420x^4 - 462x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T696	Trivial (GRH)
18.6.8882184730747543215052423168.4	x^18 + 7x^16 - 27x^14 - 245x^12 - 163x^10 + 1078x^8 + 2036x^6 + 1232x^4 + 217x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T696	Trivial (GRH)
18.18.15234636250128189842030067712.2	x^18 - 28x^16 + 301x^14 - 1566x^12 + 4200x^10 - 6167x^8 + 5060x^6 - 2261x^4 + 504x^2 - 43	\( 2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 43^{5} \)	18T696	Trivial (GRH)
18.18.29174587200611331377099546821.1	x^18 - 9x^17 + 19x^16 + 52x^15 - 232x^14 + 938x^12 - 610x^11 - 1931x^10 + 1757x^9 + 2343x^8 - 2210x^7 - 1814x^6 + 1340x^5 + 882x^4 - 316x^3 - 210x^2 + 7	\( 7^{13}\cdot 769^{4}\cdot 861043 \)	18T696	Trivial (GRH)
18.0.975771436849265818910759059456.1	x^18 + 34x^16 + 442x^14 + 2878x^12 + 10264x^10 + 20724x^8 + 24144x^6 + 15974x^4 + 5529x^2 + 769	\( -\,2^{18}\cdot 7^{12}\cdot 769^{5} \)	18T696	$[792]$ (GRH)