Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.1642535134737625976832.1	x^18 - 3x^17 + 2x^15 + 9x^14 - 3x^13 - 12x^12 - 9x^11 + 6x^10 + 17x^9 + 6x^8 - 9x^7 - 12x^6 - 3x^5 + 9x^4 + 2x^3 - 3x + 1	\( 2^{12}\cdot 3^{24}\cdot 17^{5} \)	18T400	Trivial
18.2.6568341307628680810496.1	x^18 - 3x^17 - 2x^16 + 22x^15 - 51x^14 + 57x^13 - 2x^12 - 59x^11 + 44x^10 - 13x^9 + 44x^8 - 59x^7 - 2x^6 + 57x^5 - 51x^4 + 22x^3 - 2x^2 - 3x + 1	\( 2^{12}\cdot 7^{12}\cdot 41^{5} \)	18T400	Trivial
18.6.8108488010699884287389.1	x^18 - 4x^17 + x^16 + 5x^15 + 19x^14 - 29x^13 - 36x^12 + 33x^11 + 71x^10 - 32x^9 - 94x^8 + 55x^7 + 40x^6 - 31x^5 - 4x^4 + 4x^3 + 3x^2 - 1	\( 7^{12}\cdot 13^{4}\cdot 29^{5} \)	18T400	Trivial
18.8.44348448637915901374464.1	x^18 - 3x^17 + 3x^16 - 12x^15 + 15x^14 - 6x^13 + 39x^12 + 42x^11 - 60x^10 - 2x^9 - 213x^8 - 3x^7 + 282x^6 - 15x^5 - 102x^4 - 12x^3 + 12x^2 + 6x + 1	\( -\,2^{12}\cdot 3^{27}\cdot 17^{5} \)	18T400	Trivial
18.6.474692653939173907304448.1	x^18 - 3x^17 + 3x^16 + 5x^15 - 21x^14 + 21x^13 + 29x^12 - 90x^11 + 33x^10 + 217x^9 - 537x^8 + 633x^7 - 420x^6 + 96x^5 + 144x^4 - 183x^3 + 75x^2 - 3x - 1	\( 2^{12}\cdot 3^{24}\cdot 17^{7} \)	18T400	Trivial
18.4.662714617009728033828864.1	x^18 - 3x^17 + 9x^16 - 16x^15 + 33x^14 - 69x^13 + 74x^12 - 114x^11 + 108x^10 - 205x^9 + 33x^8 - 96x^7 + 136x^6 - 24x^5 + 12x^4 - 5x^3 - 1	\( -\,2^{12}\cdot 3^{24}\cdot 17^{4}\cdot 19^{3} \)	18T400	Trivial
18.8.662714617009728033828864.1	x^18 - 9x^16 - 2x^15 + 6x^14 + 45x^13 + 11x^12 - 69x^11 + 66x^10 - 38x^9 - 27x^8 - 24x^7 - 17x^6 + 123x^5 - 21x^4 - 31x^3 + 9x^2 - 3x - 1	\( -\,2^{12}\cdot 3^{24}\cdot 17^{4}\cdot 19^{3} \)	18T400	Trivial
18.10.1370334473808280444568741.1	x^18 - 2x^17 - 13x^16 + 22x^15 + 63x^14 - 76x^13 - 168x^12 + 158x^11 + 183x^10 - 248x^9 + 68x^8 + 216x^7 - 252x^6 - 43x^5 + 76x^4 - 94x^3 - 14x^2 + 11x - 1	\( 7^{12}\cdot 13^{6}\cdot 29^{5} \)	18T400	Trivial
18.4.2781211387670060310574427.1	x^18 - 7x^17 + 14x^16 + 10x^15 - 77x^14 + 84x^13 + 93x^12 - 294x^11 + 77x^10 + 587x^9 - 910x^8 + 91x^7 + 1383x^6 - 2093x^5 + 1477x^4 - 373x^3 - 140x^2 + 91x - 13	\( -\,7^{15}\cdot 13^{4}\cdot 29^{5} \)	18T400	Trivial
18.0.6727823911885316001103872.1	x^18 - 3x^16 - 30x^14 + 52x^12 + 285x^10 + 201x^8 - 99x^6 - 51x^4 + 51x^2 + 17	\( -\,2^{24}\cdot 3^{24}\cdot 17^{5} \)	18T400	$[4]$
18.10.6727823911885316001103872.1	x^18 + 3x^16 - 30x^14 - 52x^12 + 285x^10 - 201x^8 - 99x^6 + 51x^4 + 51x^2 - 17	\( 2^{24}\cdot 3^{24}\cdot 17^{5} \)	18T400	Trivial (GRH)
18.0.26903925996047076599791616.1	x^18 + 10x^16 + 49x^14 + 179x^12 + 543x^10 + 1268x^8 + 1982x^6 + 1681x^4 + 533x^2 + 41	\( -\,2^{24}\cdot 7^{12}\cdot 41^{5} \)	18T400	$[4]$
18.6.10146939952861213092846003125.1	x^18 - 4x^17 + x^16 + 12x^15 - 12x^14 - 178x^13 + 594x^12 + 41x^11 - 1729x^10 + 3483x^9 - 1963x^8 - 7590x^7 - 3207x^6 - 11241x^5 - 4265x^4 + 1351x^3 - 1743x^2 + 1933x - 235	\( 5^{5}\cdot 13^{16}\cdot 47^{4} \)	18T400	Trivial (GRH)
18.12.58516890664476634710877708403.1	x^18 - 6x^17 - 14x^16 + 116x^15 + 103x^14 - 1025x^13 - 665x^12 + 6337x^11 - 1302x^10 - 15266x^9 + 7966x^8 + 14053x^7 - 7126x^6 - 5248x^5 + 1851x^4 + 305x^3 - 266x^2 + 16x + 1	\( -\,7^{12}\cdot 83^{5}\cdot 181^{4} \)	18T400	Trivial (GRH)
18.6.131910219387195770206998040625.1	x^18 - 6x^17 + 17x^16 - 23x^15 - 46x^14 + 179x^13 - 117x^12 - 130x^11 + 676x^10 - 1144x^9 + 1053x^8 - 1456x^7 - 793x^6 + 4684x^5 - 4158x^4 + 2265x^3 - 222x^2 - 730x - 103	\( 5^{5}\cdot 13^{17}\cdot 47^{4} \)	18T400	$[2]$ (GRH)
18.12.476906177784477015363762146875.1	x^18 - 4x^17 - 31x^16 + 185x^15 + x^14 - 1613x^13 + 1684x^12 + 6399x^11 - 10342x^10 - 11977x^9 + 28278x^8 + 5087x^7 - 35988x^6 + 11990x^5 + 16625x^4 - 11352x^3 - 303x^2 + 1678x - 317	\( -\,5^{5}\cdot 13^{16}\cdot 47^{5} \)	18T400	Trivial (GRH)
18.0.2659959427002849845011022643200000.1	x^18 + 34x^16 + 378x^14 + 1993x^12 + 5760x^10 + 9631x^8 + 9315x^6 + 4960x^4 + 1290x^2 + 125	\( -\,2^{18}\cdot 5^{5}\cdot 13^{16}\cdot 47^{4} \)	18T400	$[2, 382]$ (GRH)
18.18.2659959427002849845011022643200000.1	x^18 - 34x^16 + 378x^14 - 1993x^12 + 5760x^10 - 9631x^8 + 9315x^6 - 4960x^4 + 1290x^2 - 125	\( 2^{18}\cdot 5^{5}\cdot 13^{16}\cdot 47^{4} \)	18T400	Trivial (GRH)
18.0.3283617507769220970246128004960983.1	x^18 - 2x^17 - 25x^16 + 33x^15 + 320x^14 - 308x^13 - 1897x^12 + 797x^11 + 8545x^10 + 3048x^9 - 4524x^8 - 9069x^7 - 4129x^6 + 72083x^5 + 425870x^4 + 529829x^3 + 1004773x^2 + 752759x + 651203	\( -\,7^{12}\cdot 83^{4}\cdot 167^{3}\cdot 181^{4} \)	18T400	$[2298]$ (GRH)
18.18.66498985675071246125275566080000000.1	x^18 - 63x^16 + 1582x^14 - 20180x^12 + 137218x^10 - 471765x^8 + 671002x^6 - 144230x^4 + 8425x^2 - 125	\( 2^{18}\cdot 5^{7}\cdot 13^{16}\cdot 47^{4} \)	18T400	Trivial (GRH)