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 56)

Label	Polynomial	Discriminant	Galois group	Class group
18.4.303256405652583481344.2	x^18 - 6x^16 + 15x^14 - 23x^12 + 33x^10 - 48x^8 + 44x^6 - 15x^4 - 3x^2 + 1	\( -\,2^{30}\cdot 3^{24} \)	18T544	Trivial
18.4.3106527227728698802176.1	x^18 - 9x^17 + 42x^16 - 132x^15 + 309x^14 - 567x^13 + 842x^12 - 1035x^11 + 1080x^10 - 989x^9 + 834x^8 - 675x^7 + 520x^6 - 357x^5 + 195x^4 - 74x^3 + 12x^2 + 3x - 1	\( -\,2^{18}\cdot 3^{24}\cdot 41959 \)	18T544	Trivial
18.2.8187922952619753996288.1	x^18 + 3x^16 + 6x^12 + 9x^10 - 81x^8 - 63x^6 + 135x^4 + 81x^2 - 27	\( 2^{30}\cdot 3^{27} \)	18T544	Trivial
18.8.21781613448935042304959.1	x^18 - x^17 - 7x^16 - 4x^15 + 13x^14 + 36x^13 + 35x^12 - 5x^11 - 60x^10 - 87x^9 - 60x^8 - 5x^7 + 35x^6 + 36x^5 + 13x^4 - 4x^3 - 7x^2 - x + 1	\( -\,7^{12}\cdot 53^{6}\cdot 71 \)	18T544	Trivial
18.8.21781613448935042304959.2	x^18 - 3x^17 - 3x^16 + 15x^15 - 8x^14 - 15x^13 + 17x^12 - 3x^11 + 11x^10 - 23x^9 + 11x^8 - 3x^7 + 17x^6 - 15x^5 - 8x^4 + 15x^3 - 3x^2 - 3x + 1	\( -\,7^{12}\cdot 53^{6}\cdot 71 \)	18T544	Trivial
18.10.29757978937277452163113.1	x^18 - 7x^17 + 16x^16 - 6x^15 - 41x^14 + 97x^13 - 93x^12 - 6x^11 + 141x^10 - 205x^9 + 141x^8 - 6x^7 - 93x^6 + 97x^5 - 41x^4 - 6x^3 + 16x^2 - 7x + 1	\( 7^{12}\cdot 53^{6}\cdot 97 \)	18T544	Trivial
18.6.29757978937277452163113.1	x^18 - 4x^17 + 3x^16 + 4x^15 - 22x^14 + 34x^13 - 23x^12 - 16x^11 + 65x^10 - 85x^9 + 65x^8 - 16x^7 - 23x^6 + 34x^5 - 22x^4 + 4x^3 + 3x^2 - 4x + 1	\( 7^{12}\cdot 53^{6}\cdot 97 \)	18T544	Trivial
18.6.32470752222660638887936.1	x^18 - 9x^17 + 35x^16 - 76x^15 + 96x^14 - 56x^13 - 29x^12 + 96x^11 - 99x^10 + 44x^9 + 21x^8 - 46x^7 + 25x^6 + 6x^5 - 12x^4 + x^3 + 4x^2 - 2x - 1	\( 2^{12}\cdot 13^{12}\cdot 340261 \)	18T544	Trivial
18.4.42642877033830575780131.1	x^18 - x^17 - 2x^16 + 7x^15 - 11x^14 + 9x^13 + 4x^12 - 24x^11 + 43x^10 - 51x^9 + 43x^8 - 24x^7 + 4x^6 + 9x^5 - 11x^4 + 7x^3 - 2x^2 - x + 1	\( -\,7^{12}\cdot 53^{6}\cdot 139 \)	18T544	Trivial
18.8.42642877033830575780131.1	x^18 - 4x^17 + 3x^16 + x^15 + 7x^14 - 23x^13 + 39x^12 - 7x^11 - 20x^10 - 42x^9 - 50x^8 + 196x^7 - 176x^6 + 257x^5 - 294x^4 + 78x^3 + 128x^2 - 134x + 41	\( -\,7^{12}\cdot 53^{6}\cdot 139 \)	18T544	Trivial
18.2.155267279694122742448128.2	x^18 + 6x^16 + 6x^14 - 22x^12 - 45x^10 - 12x^8 + 7x^6 - 18x^4 - 24x^2 - 8	\( 2^{39}\cdot 3^{24} \)	18T544	Trivial
18.0.173773044728541219209931.1	x^18 - 9x^17 + 37x^16 - 92x^15 + 151x^14 - 161x^13 + 89x^12 + 25x^11 - 99x^10 + 99x^9 - 59x^8 + 21x^7 + 5x^6 - 21x^5 + 23x^4 - 14x^3 + 7x^2 - 3x + 1	\( -\,3^{6}\cdot 19^{12}\cdot 107699 \)	18T544	Trivial
18.0.249969185661440157233152.1	x^18 - 9x^17 + 53x^16 - 220x^15 + 728x^14 - 1960x^13 + 4451x^12 - 8584x^11 + 14253x^10 - 20368x^9 + 25137x^8 - 26614x^7 + 24061x^6 - 18286x^5 + 11492x^4 - 5763x^3 + 2202x^2 - 574x + 83	\( -\,2^{12}\cdot 13^{12}\cdot 599\cdot 4373 \)	18T544	Trivial
18.12.1256584347701942722269184.1	x^18 - x^16 - 25x^14 + 90x^12 - 97x^10 - 14x^8 + 81x^6 - 34x^4 - x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.12.1256584347701942722269184.2	x^18 + 7x^16 - 16x^14 - 74x^12 + 230x^10 - 172x^8 - 45x^6 + 97x^4 - 30x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.8.1256584347701942722269184.2	x^18 + 5x^16 + x^14 - 20x^12 - 13x^10 + 22x^8 + 13x^6 - 8x^4 - 3x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.12.1256584347701942722269184.3	x^18 - 6x^16 - 3x^14 + 50x^12 - 12x^10 - 89x^8 + 58x^6 + 8x^4 - 9x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.8.1256584347701942722269184.3	x^18 - x^16 - 15x^14 + 8x^12 + 70x^10 + 3x^8 - 106x^6 - 52x^4 + 8x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial
18.12.1256584347701942722269184.4	x^18 - 6x^16 - 3x^14 + 62x^12 - 60x^10 - 119x^8 + 218x^6 - 106x^4 + 13x^2 + 1	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.6.3758256635252467084296192.1	x^18 - 12x^16 + 63x^14 - 195x^12 + 399x^10 - 558x^8 + 528x^6 - 327x^4 + 117x^2 - 17	\( 2^{30}\cdot 3^{30}\cdot 17 \)	18T544	Trivial
18.10.5852021141154776996728512.1	x^18 - 3x^17 - 9x^16 + 39x^15 - 6x^14 - 129x^13 + 138x^12 + 153x^11 - 321x^10 - 38x^9 + 291x^8 - 9x^7 - 90x^6 - 66x^5 + 3x^4 + 81x^3 - 9x^2 - 30x + 1	\( 2^{6}\cdot 3^{31}\cdot 23^{6} \)	18T544	Trivial
18.8.6734506738465099277161408.1	x^18 - 7x^17 + 11x^16 + 44x^15 - 194x^14 + 177x^13 + 418x^12 - 1157x^11 + 752x^10 + 786x^9 - 1602x^8 + 1120x^7 - 475x^6 - 271x^5 + 1386x^4 - 1229x^3 - 297x^2 + 607x - 97	\( -\,2^{6}\cdot 7^{15}\cdot 53^{6} \)	18T544	Trivial
18.10.27485230939984549594007488.1	x^18 - 4x^17 - 6x^16 + 31x^15 + 17x^14 - 131x^13 + 19x^12 + 327x^11 - 292x^10 - 355x^9 + 656x^8 + 54x^7 - 586x^6 + 142x^5 + 216x^4 - 69x^3 - 25x^2 + 5x + 1	\( 2^{6}\cdot 7^{15}\cdot 67^{6} \)	18T544	Trivial (GRH)
18.16.80421398252924334225227776.1	x^18 - 10x^16 + 21x^14 + 67x^12 - 362x^10 + 621x^8 - 495x^6 + 183x^4 - 26x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.16.80421398252924334225227776.2	x^18 - 14x^16 + 77x^14 - 211x^12 + 294x^10 - 168x^8 - 30x^6 + 70x^4 - 21x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.4.80421398252924334225227776.4	x^18 + 13x^16 + 65x^14 + 146x^12 + 87x^10 - 240x^8 - 507x^6 - 362x^4 - 87x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T544	$[2]$
18.4.80421398252924334225227776.5	x^18 + x^16 - 22x^14 - 62x^12 - 8x^10 + 144x^8 + 185x^6 + 91x^4 + 18x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial
18.4.80421398252924334225227776.6	x^18 + 11x^16 + 35x^14 - 24x^12 - 383x^10 - 919x^8 - 1006x^6 - 524x^4 - 103x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T544	$[2]$
18.8.80421398252924334225227776.10	x^18 + 8x^16 + 5x^14 - 73x^12 - 62x^10 + 223x^8 + 13x^6 - 75x^4 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.8.80421398252924334225227776.11	x^18 + 5x^16 - 3x^14 - 38x^12 - 21x^10 + 53x^8 + 20x^6 - 29x^4 + 3x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.14.88133009763711378710013049.1	x^18 - 9x^17 + 24x^16 + 12x^15 - 158x^14 + 182x^13 + 237x^12 - 590x^11 + 78x^10 + 633x^9 - 417x^8 - 222x^7 + 311x^6 - 26x^5 - 86x^4 + 24x^3 + 10x^2 - 4x - 1	\( 7^{12}\cdot 53^{6}\cdot 287281 \)	18T544	Trivial (GRH)
18.14.279992823820843547402730217.3	x^18 - 2x^17 - 17x^16 + 28x^15 + 47x^14 + 21x^13 + 236x^12 - 642x^11 - 1901x^10 + 699x^9 + 4022x^8 + 2156x^7 - 1197x^6 - 1447x^5 - 298x^4 + 148x^3 + 74x^2 + 6x - 1	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T544	Trivial (GRH)
18.14.279992823820843547402730217.4	x^18 - 2x^17 - 15x^16 + 39x^15 + 94x^14 - 321x^13 - 392x^12 + 1327x^11 + 1331x^10 - 2674x^9 - 2988x^8 + 2068x^7 + 3283x^6 + 310x^5 - 1101x^4 - 800x^3 - 276x^2 + 18x + 27	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T544	Trivial (GRH)
18.6.279992823820843547402730217.6	x^18 - 5x^17 + 18x^16 - 55x^15 + 101x^14 - 86x^13 + 19x^12 + 90x^11 - 545x^10 + 1994x^9 - 5198x^8 + 9327x^7 - 10615x^6 + 7215x^5 - 1892x^4 - 2004x^3 + 2387x^2 - 712x - 41	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T544	Trivial (GRH)
18.6.279992823820843547402730217.7	x^18 - 4x^17 + 17x^16 - 39x^15 + 50x^14 - 37x^13 - 158x^12 + 269x^11 - 350x^10 + 70x^9 - 55x^8 - 263x^7 + 490x^6 - 205x^5 + 51x^4 + 102x^3 + 605x^2 + 660x - 97	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T544	Trivial (GRH)
18.10.279992823820843547402730217.8	x^18 - 4x^17 - 7x^16 + 43x^15 - 82x^14 - 34x^13 + 308x^12 - 525x^11 + 564x^10 + 534x^9 - 2063x^8 + 2838x^7 + 1297x^6 - 4579x^5 - 2106x^4 + 223x^3 + 1009x^2 + 376x - 41	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T544	Trivial (GRH)
18.6.279992823820843547402730217.8	x^18 - 4x^17 + 7x^16 - 26x^15 - 25x^14 + 164x^13 - 153x^12 - 50x^11 + 659x^10 - 182x^9 - 309x^8 + 46x^7 - 313x^6 + 548x^5 - 100x^4 + 470x^3 + 246x^2 - 1441x + 281	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T544	Trivial (GRH)
18.10.279992823820843547402730217.9	x^18 - 4x^17 + 4x^16 - 18x^15 + 43x^14 + 53x^13 - 135x^12 - 5x^11 - 312x^10 + 890x^9 - 1069x^8 + 883x^7 + 2478x^6 - 5904x^5 + 1473x^4 + 4035x^3 - 2433x^2 - 328x + 349	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T544	Trivial (GRH)
18.10.279992823820843547402730217.10	x^18 - 5x^17 + 9x^16 - 19x^15 + 13x^14 + 38x^13 + 360x^12 - 1176x^11 + 102x^10 + 3569x^9 - 7706x^8 + 9387x^7 - 4662x^6 - 4370x^5 + 11175x^4 - 10550x^3 + 4187x^2 - 339x - 97	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T544	Trivial (GRH)
18.10.279992823820843547402730217.11	x^18 - 9x^17 + 19x^16 + 52x^15 - 265x^14 + 230x^13 + 565x^12 - 1380x^11 + 1024x^10 - 70x^9 - 886x^8 + 2001x^7 - 2210x^6 + 1301x^5 - 482x^4 + 106x^3 + 28x^2 - 27x + 1	\( 7^{12}\cdot 53^{6}\cdot 97^{3} \)	18T544	Trivial (GRH)
18.14.374529353033905727790624768.2	x^18 - 9x^16 - 3x^14 + 255x^12 - 936x^10 + 1251x^8 - 510x^6 - 18x^4 + 36x^2 - 3	\( 2^{12}\cdot 3^{31}\cdot 23^{6} \)	18T544	Trivial (GRH)
18.10.431008431261766353738330112.2	x^18 + 7x^16 - 63x^14 - 112x^12 + 1421x^10 - 2695x^8 - 98x^6 + 4116x^4 - 2401x^2 - 343	\( 2^{12}\cdot 7^{15}\cdot 53^{6} \)	18T544	Trivial (GRH)
18.12.1244874949141023786770214912.1	x^18 - 9x^17 + 33x^16 - 60x^15 + 33x^14 + 105x^13 - 297x^12 + 339x^11 - 96x^10 - 268x^9 + 417x^8 - 231x^7 - 39x^6 + 129x^5 - 57x^4 - 15x^3 + 15x^2 - 1	\( -\,2^{12}\cdot 3^{30}\cdot 7^{6}\cdot 12547 \)	18T544	Trivial (GRH)
18.0.7123576667122313292544004096.1	x^18 - 3x^17 + 12x^16 - 33x^15 + 116x^14 - 218x^13 + 611x^12 - 1097x^11 + 2554x^10 - 3133x^9 + 7272x^8 - 7520x^7 + 14017x^6 - 5399x^5 + 13806x^4 - 961x^3 + 12432x^2 + 2636x + 5144	\( -\,2^{12}\cdot 7^{12}\cdot 53^{6}\cdot 5669 \)	18T544	$[2, 48]$ (GRH)
18.2.7800875630533660419847094272.1	x^18 + 15x^16 + 88x^14 + 237x^12 + 178x^10 - 581x^8 - 1644x^6 - 1695x^4 - 743x^2 - 97	\( 2^{18}\cdot 7^{12}\cdot 53^{6}\cdot 97 \)	18T544	$[4]$
18.18.14556273083779304494766227456.1	x^18 - 21x^16 + 184x^14 - 883x^12 + 2554x^10 - 4605x^8 + 5156x^6 - 3439x^4 + 1233x^2 - 181	\( 2^{18}\cdot 7^{12}\cdot 53^{6}\cdot 181 \)	18T544	Trivial (GRH)
18.2.23969878594169966578599985152.1	x^18 + 15x^16 + 60x^14 + 42x^12 - 225x^10 - 549x^8 - 510x^6 - 225x^4 - 45x^2 - 3	\( 2^{18}\cdot 3^{31}\cdot 23^{6} \)	18T544	$[2]$ (GRH)
18.18.64776183469527747581046896381.1	x^18 - 9x^17 + 15x^16 + 84x^15 - 278x^14 - 238x^13 + 1595x^12 - 2x^11 - 4830x^10 + 1193x^9 + 8957x^8 - 2006x^7 - 10587x^6 + 398x^5 + 7424x^4 + 1722x^3 - 2206x^2 - 1233x - 181	\( 7^{12}\cdot 53^{6}\cdot 211146389 \)	18T544	Trivial (GRH)
18.12.1280976322666113476586551144448.1	x^18 - 3x^17 - 6x^16 + 36x^15 - 195x^14 + 495x^13 + 1074x^12 - 6525x^11 + 2898x^10 + 26211x^9 - 23400x^8 - 49365x^7 + 29328x^6 + 47691x^5 + 5715x^4 - 19314x^3 - 9972x^2 + 2799x + 1731	\( -\,2^{12}\cdot 3^{31}\cdot 7^{9}\cdot 12547 \)	18T544	$[2]$ (GRH)
18.6.5489864954254481311949195575296.1	x^18 + 9x^16 + 18x^14 - 48x^12 - 216x^10 - 198x^8 + 129x^6 + 261x^4 + 72x^2 - 19	\( 2^{18}\cdot 3^{32}\cdot 19\cdot 29^{6} \)	18T544	Trivial (GRH)