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 48 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.4.225073641557765238784.1	x^18 - x^16 - 2x^15 + x^14 - 3x^13 - x^12 + 8x^11 + x^10 - 4x^9 - x^8 + 10x^7 + 8x^6 - 17x^5 - 14x^4 + 8x^3 + 7x^2 - x - 1	\( -\,2^{12}\cdot 7^{12}\cdot 13^{4}\cdot 139 \)	18T766	Trivial (GRH)
18.4.9430423657787228422144.1	x^18 - 6x^17 + 15x^16 - 24x^15 + 36x^14 - 34x^13 - 53x^12 + 260x^11 - 489x^10 + 584x^9 - 479x^8 + 268x^7 - 81x^6 - 38x^5 + 58x^4 - 10x^3 - 10x^2 + 2x + 1	\( -\,2^{18}\cdot 7^{13}\cdot 13^{5} \)	18T766	Trivial
18.2.14404713059696975282176.1	x^18 - 4x^17 + 30x^15 - 69x^14 + 36x^13 + 91x^12 - 160x^11 + 39x^10 + 144x^9 - 170x^8 + 58x^7 + 24x^6 - 40x^5 + 31x^4 - 18x^3 + 11x^2 - 4x + 1	\( 2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 139 \)	18T766	Trivial
18.6.15027557693241115871569.1	x^18 - 5x^17 + 14x^16 - 39x^15 + 88x^14 - 133x^13 + 148x^12 - 154x^11 + 179x^10 - 210x^9 + 198x^8 - 140x^7 + 99x^6 - 84x^5 + 63x^4 - 36x^3 + 9x^2 + 2x - 1	\( 7^{14}\cdot 43^{4}\cdot 6481 \)	18T766	Trivial (GRH)
18.0.34229005099925175414784.1	x^18 - 9x^17 + 41x^16 - 124x^15 + 278x^14 - 490x^13 + 703x^12 - 838x^11 + 837x^10 - 698x^9 + 477x^8 - 256x^7 + 103x^6 - 34x^5 + 22x^4 - 23x^3 + 16x^2 - 6x + 1	\( -\,2^{12}\cdot 7^{12}\cdot 13^{4}\cdot 21139 \)	18T766	Trivial
18.2.46426701084490970693632.1	x^18 - x^16 - x^14 + 12x^12 - 26x^10 + 31x^8 - 29x^6 + 7x^4 - 7	\( 2^{24}\cdot 7^{13}\cdot 13^{4} \)	18T766	Trivial
18.6.86221016299768945573888.2	x^18 - 3x^16 - x^14 + 10x^12 - 43x^8 + 89x^6 - 91x^4 + 52x^2 - 13	\( 2^{24}\cdot 7^{12}\cdot 13^{5} \)	18T766	Trivial (GRH)
18.0.105192903852687811100983.1	x^18 - 4x^17 + 6x^16 - 3x^15 + 7x^14 - 28x^13 + 43x^12 - 28x^11 + 11x^10 - 33x^8 + 70x^7 - 55x^6 - 14x^5 + 70x^4 - 68x^3 + 34x^2 - 9x + 1	\( -\,7^{15}\cdot 43^{4}\cdot 6481 \)	18T766	$[2]$
18.10.2415964169284813676020898133.1	x^18 - 6x^17 + 55x^15 - 78x^14 - 84x^13 + 216x^12 - 153x^11 + 252x^10 - 137x^9 - 801x^8 + 1440x^7 - 678x^6 - 627x^5 + 1248x^4 - 943x^3 + 384x^2 - 84x + 8	\( 3^{18}\cdot 7^{14}\cdot 13\cdot 29^{4} \)	18T766	Trivial (GRH)
18.14.2415964169284813676020898133.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 147x^14 + 525x^13 - 722x^12 - 387x^11 + 2721x^10 - 3408x^9 - 21x^8 + 5511x^7 - 5795x^6 - 804x^5 + 4320x^4 - 1800x^3 - 384x^2 + 384x - 64	\( 3^{18}\cdot 7^{14}\cdot 13\cdot 29^{4} \)	18T766	Trivial (GRH)
18.10.2415964169284813676020898133.2	x^18 - 3x^17 + 6x^16 + 11x^15 - 87x^14 + 105x^13 + 34x^12 - 444x^11 + 708x^10 + 256x^9 - 1152x^8 + 1695x^7 + 1014x^6 - 3843x^5 - 2400x^4 + 1884x^3 + 2145x^2 + 678x + 71	\( 3^{18}\cdot 7^{14}\cdot 13\cdot 29^{4} \)	18T766	Trivial (GRH)
18.14.5389458531481507431123541989.1	x^18 - 9x^17 + 15x^16 + 70x^15 - 216x^14 - 102x^13 + 752x^12 - 117x^11 - 1089x^10 + 35x^9 + 1098x^8 + 480x^7 - 1207x^6 - 285x^5 + 807x^4 - 141x^3 - 147x^2 + 63x - 7	\( 3^{18}\cdot 7^{14}\cdot 29^{5} \)	18T766	Trivial (GRH)
18.6.5389458531481507431123541989.2	x^18 + 12x^16 + 18x^14 - 258x^12 - 1053x^10 - 642x^8 + 1919x^6 + 1617x^4 - 753x^2 - 29	\( 3^{18}\cdot 7^{14}\cdot 29^{5} \)	18T766	Trivial (GRH)
18.12.11893977448786775020410575424.1	x^18 - 9x^17 + 18x^16 + 59x^15 - 258x^14 + 57x^13 + 1022x^12 - 1308x^11 - 1302x^10 + 3746x^9 - 966x^8 - 3975x^7 + 3619x^6 + 981x^5 - 2367x^4 + 514x^3 + 87x^2 - 9x - 1	\( -\,2^{6}\cdot 3^{18}\cdot 7^{14}\cdot 29^{4} \)	18T766	Trivial (GRH)
18.8.11893977448786775020410575424.2	x^18 - 9x^17 + 24x^16 + 9x^15 - 159x^14 + 306x^13 - 217x^12 - 96x^11 + 474x^10 - 824x^9 + 948x^8 - 384x^7 - 1736x^6 + 4896x^5 - 5088x^4 + 576x^3 + 3072x^2 - 2304x + 512	\( -\,2^{6}\cdot 3^{18}\cdot 7^{14}\cdot 29^{4} \)	18T766	Trivial (GRH)
18.12.13194881232247828538267982111.1	x^18 - 3x^17 - 21x^16 + 65x^15 + 93x^14 - 513x^13 + 192x^12 + 1431x^11 - 1626x^10 - 1504x^9 + 2949x^8 + 549x^7 - 2334x^6 - 93x^5 + 852x^4 + 100x^3 - 105x^2 - 24x - 1	\( -\,3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 71 \)	18T766	Trivial (GRH)
18.4.13194881232247828538267982111.1	x^18 - 9x^17 + 66x^16 - 324x^15 + 1281x^14 - 4011x^13 + 10249x^12 - 21441x^11 + 36771x^10 - 51591x^9 + 58992x^8 - 54633x^7 + 40564x^6 - 23766x^5 + 10722x^4 - 3585x^3 + 834x^2 - 120x + 8	\( -\,3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 71 \)	18T766	Trivial (GRH)
18.8.13194881232247828538267982111.1	x^18 - 6x^17 + 3x^16 + 67x^15 - 231x^14 + 168x^13 + 853x^12 - 2631x^11 + 2658x^10 + 1438x^9 - 8085x^8 + 12264x^7 - 10081x^6 + 3801x^5 + 699x^4 - 1493x^3 + 552x^2 + 144x - 113	\( -\,3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 71 \)	18T766	Trivial (GRH)
18.8.15425002003895348854594965003.1	x^18 - 9x^17 + 21x^16 + 22x^15 - 120x^14 + 27x^13 + 145x^12 + 84x^11 - 30x^10 - 604x^9 + 63x^8 + 975x^7 - 62x^6 - 705x^5 + 489x^4 + 375x^3 - 243x^2 - 99x + 13	\( -\,3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 83 \)	18T766	Trivial (GRH)
18.4.16911749184993695732146286931.1	x^18 - 6x^17 + 30x^16 - 98x^15 + 258x^14 - 525x^13 + 706x^12 - 426x^11 - 777x^10 + 3140x^9 - 6033x^8 + 8223x^7 - 8413x^6 + 5547x^5 - 621x^4 - 3547x^3 + 4965x^2 - 3390x + 953	\( -\,3^{18}\cdot 7^{15}\cdot 13\cdot 29^{4} \)	18T766	$[2]$ (GRH)
18.6.21000303933014149645412422233.1	x^18 - 3x^17 - 15x^16 + 42x^15 + 33x^14 - 48x^13 - 199x^12 + 114x^11 + 93x^10 + 139x^9 + 186x^8 + 456x^7 - 1592x^6 - 768x^5 + 1056x^4 + 2688x^3 - 1920x^2 - 768x + 512	\( 3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 113 \)	18T766	Trivial (GRH)
18.8.25832232271583776997454218499.1	x^18 - 9x^16 - 17x^15 + 18x^14 + 285x^13 - 111x^12 - 1464x^11 + 648x^10 + 4500x^9 - 4254x^8 - 4875x^7 + 8868x^6 - 2415x^5 - 3648x^4 + 4021x^3 - 1818x^2 + 165x + 113	\( -\,3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 139 \)	18T766	Trivial (GRH)
18.12.31035847405427991068883845247.1	x^18 - 15x^16 + 15x^14 + 659x^12 - 2868x^10 + 165x^8 + 14645x^6 - 15477x^4 - 3081x^2 + 167	\( -\,3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 167 \)	18T766	Trivial (GRH)
18.8.31035847405427991068883845247.1	x^18 + 21x^16 + 129x^14 + 22x^12 - 1740x^10 - 1419x^8 + 7524x^6 - 4878x^4 + 180x^2 + 167	\( -\,3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 167 \)	18T766	Trivial (GRH)
18.12.31035847405427991068883845247.2	x^18 - 9x^17 + 36x^16 - 84x^15 + 45x^14 + 441x^13 - 1730x^12 + 3477x^11 - 3741x^10 + 60x^9 + 4836x^8 - 4233x^7 - 489x^6 + 2220x^5 - 678x^4 - 368x^3 + 165x^2 + 51x + 1	\( -\,3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 167 \)	18T766	Trivial (GRH)
18.8.31035847405427991068883845247.2	x^18 - 3x^17 - 12x^16 + 88x^15 - 174x^14 + 9x^13 + 704x^12 - 1680x^11 + 1734x^10 + 968x^9 - 3804x^8 + 393x^7 + 5413x^6 - 780x^5 - 7596x^4 + 1576x^3 + 4032x^2 - 672x - 448	\( -\,3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 167 \)	18T766	Trivial (GRH)
18.10.33637654972350098104598658621.1	x^18 - 6x^17 + 9x^16 + 7x^15 - 60x^14 + 147x^13 - 141x^12 + 183x^11 + 642x^10 - 3095x^9 + 432x^8 + 2742x^7 + 2316x^6 + 11193x^5 - 18621x^4 - 20995x^3 + 27723x^2 + 9855x - 12319	\( 3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 181 \)	18T766	Trivial (GRH)
18.6.33637654972350098104598658621.1	x^18 - 9x^17 + 24x^16 + 8x^15 - 117x^14 + 461x^12 + 822x^11 - 6489x^10 + 8099x^9 + 16068x^8 - 56421x^7 + 38002x^6 + 69216x^5 - 133350x^4 + 48965x^3 + 58212x^2 - 59892x + 15673	\( 3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 181 \)	18T766	Trivial (GRH)
18.6.33637654972350098104598658621.2	x^18 - 6x^17 + 6x^16 + 59x^15 - 207x^14 + 36x^13 + 975x^12 - 1191x^11 - 2697x^10 + 5814x^9 + 5004x^8 - 16446x^7 - 5903x^6 + 28578x^5 + 12351x^4 - 29367x^3 - 21324x^2 + 14013x + 11087	\( 3^{18}\cdot 7^{14}\cdot 29^{4}\cdot 181 \)	18T766	Trivial (GRH)
18.10.281041488075161284097055916032.1	x^18 - 12x^16 - 2x^15 + 111x^14 + 66x^13 - 1112x^12 - 2910x^11 + 996x^10 + 17366x^9 + 32466x^8 + 10296x^7 - 55584x^6 - 107592x^5 - 95673x^4 - 47316x^3 - 13008x^2 - 1812x - 97	\( 2^{18}\cdot 3^{18}\cdot 7^{13}\cdot 13^{4} \)	18T766	Trivial (GRH)
18.10.344925346014816475591906687296.1	x^18 - 3x^17 - 18x^16 + 96x^15 - 87x^14 - 345x^13 + 1005x^12 - 378x^11 - 2283x^10 + 2638x^9 + 3009x^8 - 1986x^7 - 2252x^6 + 339x^5 + 678x^4 - 3x^3 - 72x^2 + 3x + 1	\( 2^{6}\cdot 3^{18}\cdot 7^{14}\cdot 29^{5} \)	18T766	Trivial (GRH)
18.14.344925346014816475591906687296.1	x^18 - 9x^17 + 9x^16 + 129x^15 - 390x^14 - 90x^13 + 1461x^12 - 942x^11 - 1635x^10 + 1579x^9 + 519x^8 - 786x^7 - 5x^6 + 345x^5 - 120x^4 - 88x^3 + 24x^2 + 6x - 1	\( 2^{6}\cdot 3^{18}\cdot 7^{14}\cdot 29^{5} \)	18T766	Trivial (GRH)
18.2.344925346014816475591906687296.1	x^18 - 27x^15 - 3x^14 - 57x^13 + 19x^12 - 492x^11 + 714x^10 + 4068x^9 + 12999x^8 + 858x^7 + 6029x^6 - 33933x^5 + 77940x^4 - 18689x^3 + 19278x^2 - 12243x + 1757	\( 2^{6}\cdot 3^{18}\cdot 7^{14}\cdot 29^{5} \)	18T766	Trivial (GRH)
18.10.521934192139585241894532415488.1	x^18 + 3x^16 - 120x^14 - 305x^12 + 3855x^10 + 8391x^8 - 24581x^6 - 2262x^4 + 780x^2 - 13	\( 2^{18}\cdot 3^{18}\cdot 7^{12}\cdot 13^{5} \)	18T766	Trivial (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)
18.16.2414477422103715329143346811072.1	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)
18.4.2414477422103715329143346811072.1	x^18 - 9x^17 + 39x^16 - 75x^15 - 24x^14 + 396x^13 - 282x^12 - 1977x^11 + 4701x^10 + 567x^9 - 12672x^8 + 6813x^7 + 25784x^6 - 31554x^5 - 12759x^4 + 35943x^3 - 5394x^2 - 9534x - 601	\( -\,2^{6}\cdot 3^{18}\cdot 7^{15}\cdot 29^{5} \)	18T766	$[2, 2]$ (GRH)
18.14.2414477422103715329143346811072.1	x^18 - 6x^17 - 9x^16 + 116x^15 - 18x^14 - 693x^13 + 287x^12 + 1485x^11 - 552x^10 - 520x^9 - 549x^8 - 1530x^7 + 2128x^6 + 1197x^5 - 1377x^4 - 152x^3 + 171x^2 + 15x - 1	\( 2^{6}\cdot 3^{18}\cdot 7^{15}\cdot 29^{5} \)	18T766	Trivial (GRH)
18.6.2414477422103715329143346811072.1	x^18 - 6x^17 - 6x^16 + 147x^15 - 219x^14 - 1230x^13 + 2972x^12 + 5445x^11 - 19848x^10 - 8259x^9 + 79359x^8 - 46203x^7 - 137394x^6 + 175326x^5 + 68934x^4 - 202983x^3 + 37485x^2 + 96579x - 48539	\( 2^{6}\cdot 3^{18}\cdot 7^{15}\cdot 29^{5} \)	18T766	Trivial (GRH)
18.12.3653539344977096693261726908416.1	x^18 - 3x^17 - 33x^16 + 79x^15 + 357x^14 - 849x^13 - 1027x^12 + 5988x^11 - 4134x^10 - 32614x^9 + 13254x^8 + 88404x^7 + 36276x^6 - 23808x^5 + 20760x^4 + 19416x^3 - 37560x^2 - 38232x - 9512	\( -\,2^{18}\cdot 3^{18}\cdot 7^{13}\cdot 13^{5} \)	18T766	Trivial (GRH)
18.4.3653539344977096693261726908416.1	x^18 - 15x^16 - 32x^15 + 102x^14 + 234x^13 - 241x^12 - 642x^11 + 2553x^10 + 2754x^9 - 12477x^8 - 19110x^7 - 3967x^6 + 20826x^5 + 60840x^4 + 121238x^3 + 268086x^2 + 295230x + 88829	\( -\,2^{18}\cdot 3^{18}\cdot 7^{13}\cdot 13^{5} \)	18T766	$[2]$ (GRH)
18.12.5328501897056475209143937789952.1	x^18 - 15x^16 - 27x^14 + 832x^12 - 2484x^10 + 1875x^8 + 890x^6 - 1218x^4 + 168x^2 + 7	\( -\,2^{12}\cdot 3^{18}\cdot 7^{15}\cdot 29^{4} \)	18T766	Trivial (GRH)
18.2.5328501897056475209143937789952.1	x^18 + 33x^16 + 375x^14 + 1546x^12 - 495x^10 - 17973x^8 - 38562x^6 - 24339x^4 - 3843x^2 - 7	\( 2^{12}\cdot 3^{18}\cdot 7^{15}\cdot 29^{4} \)	18T766	$[4]$ (GRH)
18.6.17986655236810322182211578626048.1	x^18 + 24x^16 + 117x^14 - 485x^12 - 3597x^10 - 6210x^8 - 2934x^6 + 567x^4 + 273x^2 - 7	\( 2^{24}\cdot 3^{18}\cdot 7^{13}\cdot 13^{4} \)	18T766	Trivial (GRH)
18.18.22075222144948254437882027986944.1	x^18 - 60x^16 + 1437x^14 - 18180x^12 + 134376x^10 - 600042x^8 + 1596029x^6 - 2340996x^4 + 1500576x^2 - 90944	\( 2^{12}\cdot 3^{18}\cdot 7^{14}\cdot 29^{5} \)	18T766	Trivial (GRH)
18.18.70019845241007744545157057521088.1	x^18 - 6x^17 - 39x^16 + 288x^15 + 228x^14 - 3564x^13 + 245x^12 + 20271x^11 - 4368x^10 - 61071x^9 + 8136x^8 + 98508x^7 + 1667x^6 - 78813x^5 - 11949x^4 + 25836x^3 + 5586x^2 - 1620x + 83	\( 2^{6}\cdot 3^{18}\cdot 7^{15}\cdot 29^{6} \)	18T766	Trivial (GRH)
18.0.154526555014637781065174195908608.1	x^18 - 3x^17 + 3x^16 + 20x^15 - 48x^14 - 153x^13 + 869x^12 + 4968x^11 + 12933x^10 + 23132x^9 + 35334x^8 + 49026x^7 + 56811x^6 + 50841x^5 + 41094x^4 + 31743x^3 + 18630x^2 + 6858x + 4509	\( -\,2^{12}\cdot 3^{18}\cdot 7^{15}\cdot 29^{5} \)	18T766	$[2, 4, 48]$ (GRH)
18.0.233826518078534188368750522138624.1	x^18 + 51x^16 + 1071x^14 + 11870x^12 + 73542x^10 + 245253x^8 + 371727x^6 + 135135x^4 + 9828x^2 + 91	\( -\,2^{24}\cdot 3^{18}\cdot 7^{13}\cdot 13^{5} \)	18T766	$[2, 2, 112]$ (GRH)