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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.92225142947365783203125.1	x^18 + 2x^16 - 3x^15 - 14x^14 + 18x^13 - 79x^12 + 154x^11 - 297x^10 + 475x^9 - 701x^8 + 794x^7 - 869x^6 + 586x^5 - 428x^4 + 108x^3 + 54x^2 - 23x - 19	\( 5^{9}\cdot 241^{7} \)	18T626	$[2]$
18.2.1950669441431215786950656.1	x^18 - 4x^17 - 4x^16 + 12x^15 + 61x^14 - 114x^13 - 95x^12 + 236x^11 + 187x^10 - 640x^9 + 150x^8 + 822x^7 - 934x^6 + 218x^5 + 227x^4 - 116x^3 - 41x^2 - 1	\( 2^{18}\cdot 13^{7}\cdot 17^{9} \)	18T626	$[2]$ (GRH)
18.4.3882077770175991570051072.1	x^18 + 6x^16 + 21x^14 - 63x^12 - 330x^10 - 516x^8 - 300x^6 + 42x^4 + 129x^2 + 43	\( -\,2^{12}\cdot 3^{20}\cdot 43^{7} \)	18T626	Trivial
18.0.3882077770175991570051072.2	x^18 + 9x^16 + 3x^14 - 48x^12 + 21x^10 + 267x^8 + 444x^6 + 396x^4 + 195x^2 + 43	\( -\,2^{12}\cdot 3^{20}\cdot 43^{7} \)	18T626	Trivial
18.4.3882077770175991570051072.2	x^18 - 3x^16 + 15x^14 - 72x^12 + 66x^10 + 57x^8 - 21x^6 - 75x^4 - 12x^2 + 43	\( -\,2^{12}\cdot 3^{20}\cdot 43^{7} \)	18T626	Trivial
18.0.3882077770175991570051072.3	x^18 + 12x^16 + 63x^14 + 189x^12 + 348x^10 + 387x^8 + 231x^6 + 39x^4 + 43	\( -\,2^{12}\cdot 3^{20}\cdot 43^{7} \)	18T626	Trivial
18.10.212255571425554456785711792128.1	x^18 - 4x^17 - 10x^16 + 20x^15 + 12x^14 + 168x^13 - 327x^12 - 572x^11 + 939x^10 - 2130x^9 + 6319x^8 - 7614x^7 + 5595x^6 - 220x^5 - 5796x^4 + 3402x^3 + 595x^2 - 344x - 53	\( 2^{18}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.14.212255571425554456785711792128.1	x^18 - 8x^17 + 9x^16 + 98x^15 - 222x^14 - 492x^13 + 1202x^12 + 1384x^11 - 2593x^10 - 2166x^9 + 2039x^8 + 1752x^7 + 629x^6 - 648x^5 - 1828x^4 + 88x^3 + 868x^2 - 8x - 104	\( 2^{18}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.6.212255571425554456785711792128.1	x^18 - 2x^17 - 20x^16 + 16x^15 + 165x^14 + 18x^13 - 667x^12 - 228x^11 + 1056x^10 - 1238x^9 + 2772x^8 - 1416x^7 - 17680x^6 + 28870x^5 + 6064x^4 - 3020x^3 - 5181x^2 - 1142x + 1021	\( 2^{18}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.10.212255571425554456785711792128.2	x^18 - 2x^17 - 6x^16 + 36x^15 - 32x^14 - 124x^13 + 234x^12 - 440x^11 - 460x^10 + 2452x^9 + 498x^8 - 4074x^7 + 1411x^6 + 632x^5 - 946x^4 + 864x^3 - 366x^2 + 50x + 1	\( 2^{18}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.14.212255571425554456785711792128.2	x^18 + x^16 - 146x^14 + 1036x^12 - 2639x^10 + 529x^8 + 10053x^6 - 19063x^4 + 13015x^2 - 2603	\( 2^{18}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.6.212255571425554456785711792128.2	x^18 - 8x^17 + 36x^16 - 108x^15 + 282x^14 - 672x^13 + 473x^12 + 3984x^11 - 17964x^10 + 43864x^9 - 75841x^8 + 93244x^7 - 70983x^6 + 17692x^5 + 20504x^4 - 20516x^3 + 6116x^2 - 216x - 104	\( 2^{18}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.10.212255571425554456785711792128.3	x^18 - x^16 - 4x^15 - 69x^14 - 96x^13 + 50x^12 + 80x^11 - 58x^10 + 288x^9 + 589x^8 - 356x^7 - 345x^6 + 228x^5 - 221x^4 - 160x^3 + 20x^2 + 8x - 1	\( 2^{18}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.6.212255571425554456785711792128.3	x^18 - 2x^17 - 14x^16 + 56x^15 - 57x^14 - 248x^13 + 896x^12 - 474x^11 - 2976x^10 + 4072x^9 + 3940x^8 - 10362x^7 - 4655x^6 + 29574x^5 + 8498x^4 - 40796x^3 + 5272x^2 + 1728x - 776	\( 2^{18}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.10.212255571425554456785711792128.4	x^18 - 2x^16 - 143x^14 - 29x^12 + 2663x^10 - 2220x^8 - 14366x^6 + 28265x^4 - 12467x^2 - 2603	\( 2^{18}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.10.13584356571235485234285554696192.1	x^18 - 4x^17 + 20x^15 - 139x^14 + 938x^13 - 2513x^12 + 856x^11 + 9317x^10 - 26280x^9 + 31698x^8 + 39076x^7 - 161528x^6 + 16434x^5 + 241901x^4 + 3840x^3 - 105919x^2 - 22202x + 3821	\( 2^{24}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.18.13584356571235485234285554696192.1	x^18 - 27x^16 + 310x^14 - 1980x^12 + 7717x^10 - 18919x^8 + 28965x^6 - 26487x^4 + 13015x^2 - 2603	\( 2^{24}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.2.13584356571235485234285554696192.1	x^18 - 6x^17 + 20x^16 - 36x^15 + 38x^14 - 2x^13 - 54x^12 + 384x^11 - 1363x^10 + 4148x^9 - 6508x^8 + 170x^7 + 23741x^6 - 36270x^5 - 34892x^4 + 195188x^3 - 273668x^2 + 120296x + 58024	\( 2^{24}\cdot 19^{7}\cdot 137^{7} \)	18T626	$[2, 12]$ (GRH)
18.6.13584356571235485234285554696192.1	x^18 - 4x^17 - 4x^16 - 6x^15 + 47x^14 + 410x^13 - 870x^12 + 568x^11 - 6617x^10 + 14536x^9 - 9372x^8 + 50818x^7 - 87263x^6 + 173098x^5 - 145586x^4 + 219588x^3 - 258096x^2 + 102288x - 11432	\( 2^{24}\cdot 19^{7}\cdot 137^{7} \)	18T626	$[2, 2]$ (GRH)
18.10.13584356571235485234285554696192.2	x^18 - x^16 - 143x^14 + 496x^12 + 2124x^10 - 8045x^8 - 2993x^6 + 16663x^4 + 6302x^2 - 2603	\( 2^{24}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)
18.2.13584356571235485234285554696192.2	x^18 + 32x^16 + 344x^14 + 1135x^12 - 3249x^10 - 27037x^8 - 56503x^6 - 51256x^4 - 20321x^2 - 2603	\( 2^{24}\cdot 19^{7}\cdot 137^{7} \)	18T626	$[2, 16]$ (GRH)
18.18.869398820559071054994275500556288.1	x^18 - 57x^16 + 1310x^14 - 15871x^12 + 110420x^10 - 448396x^8 + 1030592x^6 - 1248320x^4 + 736512x^2 - 166592	\( 2^{30}\cdot 19^{7}\cdot 137^{7} \)	18T626	Trivial (GRH)