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
18.0.228289854753724432384.1	x^18 - 2x^14 - 5x^10 + 9x^8 - 2x^6 + 2x^4 - 3x^2 + 1	\( -\,2^{18}\cdot 101^{2}\cdot 292181^{2} \)	18T913	Trivial
18.0.237081221621518434304.1	x^18 + 2x^14 + 2x^12 + 5x^10 + 6x^8 + 5x^6 + 5x^4 + 2x^2 + 1	\( -\,2^{18}\cdot 353^{2}\cdot 85193^{2} \)	18T913	Trivial
18.2.1700891962302658203125.1	x^18 - 2x^17 + 2x^16 + 4x^15 - 17x^14 + 53x^13 - 64x^12 + 54x^11 - 28x^10 + 13x^9 + 9x^8 + 42x^7 + x^6 + 3x^5 - 13x^4 - 14x^3 - 9x^2 - 3x - 1	\( 5^{9}\cdot 101^{2}\cdot 292181^{2} \)	18T913	Trivial
18.0.3165035193944739414016.1	x^18 + 2x^16 - x^14 - 3x^12 + 9x^10 + 27x^8 + 23x^6 + 10x^4 + 4x^2 + 1	\( -\,2^{18}\cdot 367^{2}\cdot 299401^{2} \)	18T913	Trivial
18.0.3261581939814810517504.1	x^18 + 3x^16 + 3x^14 + 3x^12 + 4x^10 + 5x^8 + 8x^6 + 3x^4 - 2x^2 + 1	\( -\,2^{18}\cdot 111543479^{2} \)	18T913	Trivial
18.6.23581349804585720703125.1	x^18 - 2x^17 - x^16 + 6x^15 - 14x^14 - 12x^13 + 58x^12 + 73x^11 - 67x^10 - 207x^9 - 158x^8 - 10x^7 + 69x^6 + 41x^5 - 11x^4 - 12x^3 + 4x^2 + 2x - 1	\( 5^{9}\cdot 367^{2}\cdot 299401^{2} \)	18T913	Trivial
18.0.53977668015744910360576.1	x^18 + 7x^16 + 19x^14 + 23x^12 + 4x^10 - 19x^8 - 12x^6 + 7x^4 + 6x^2 + 1	\( -\,2^{18}\cdot 453771377^{2} \)	18T913	Trivial
18.0.54463704731702620585984.1	x^18 - 6x^14 - x^12 + 17x^10 + 30x^8 + 35x^6 + 24x^4 + 8x^2 + 1	\( -\,2^{18}\cdot 109^{2}\cdot 4181741^{2} \)	18T913	Trivial
18.10.402164965985304939453125.1	x^18 - x^17 - 10x^16 + 9x^15 + 32x^14 - 12x^13 - 34x^12 - 81x^11 - 41x^10 + 173x^9 + 109x^8 - 111x^7 - 63x^6 + 22x^5 - 2x^4 + 9x^2 - 1	\( 5^{9}\cdot 453771377^{2} \)	18T913	Trivial (GRH)
18.0.1821632477226108224536576.1	x^18 + 8x^16 + 18x^14 - x^12 - 43x^10 - 22x^8 + 43x^6 + 44x^4 + 12x^2 + 1	\( -\,2^{18}\cdot 2791^{2}\cdot 944497^{2} \)	18T913	Trivial
18.0.1846628829566101684706067.1	x^18 - 2x^17 + 11x^16 - 6x^15 + 54x^14 - 25x^13 + 153x^12 - 31x^11 + 268x^10 - 56x^9 + 290x^8 - 18x^7 + 176x^6 - 32x^5 + 56x^4 - 8x^3 + 11x^2 - 2x + 1	\( -\,3^{9}\cdot 9685993193^{2} \)	18T913	$[6]$
18.0.2047104877383620556488704.1	x^18 + 9x^16 + 24x^14 + 6x^12 - 50x^10 - 37x^8 + 38x^6 + 47x^4 + 14x^2 + 1	\( -\,2^{18}\cdot 23^{2}\cdot 5569^{2}\cdot 21817^{2} \)	18T913	Trivial
18.14.13572219589547129158203125.1	x^18 - 2x^17 - 10x^16 + 8x^15 + 29x^14 + 46x^13 + 23x^12 - 231x^11 - 237x^10 + 224x^9 + 201x^8 - 78x^7 + 19x^6 + 17x^5 - 64x^4 - 4x^3 + 18x^2 - 1	\( 5^{9}\cdot 2791^{2}\cdot 944497^{2} \)	18T913	Trivial (GRH)
18.0.36374607805480156224815104.1	x^18 + 18x^16 + 125x^14 + 434x^12 + 818x^10 + 861x^8 + 509x^6 + 162x^4 + 24x^2 + 1	\( -\,2^{18}\cdot 11779563529^{2} \)	18T913	$[15]$
18.18.183239187763363936033203125.1	x^18 - 2x^17 - 25x^16 + 26x^15 + 214x^14 - 115x^13 - 823x^12 + 231x^11 + 1560x^10 - 284x^9 - 1556x^8 + 238x^7 + 826x^6 - 122x^5 - 220x^4 + 30x^3 + 25x^2 - 2x - 1	\( 5^{9}\cdot 9685993193^{2} \)	18T913	Trivial (GRH)
18.10.41224468721177639474720732921.1	x^18 - 3x^17 + 5x^16 + x^15 - 164x^14 + 432x^13 - 826x^12 - 2375x^11 + 15739x^10 - 10896x^9 - 43958x^8 + 158094x^7 - 37363x^6 - 657180x^5 + 191202x^4 + 1207011x^3 + 74572x^2 - 827552x - 325399	\( 41^{9}\cdot 11221481^{2} \)	18T913	Trivial (GRH)
18.2.93367623828446393959890781661.1	x^18 - 2x^17 - 49x^16 + 84x^15 + 1320x^14 - 2349x^13 - 23537x^12 + 38942x^11 + 309106x^10 - 369935x^9 - 2888104x^8 + 1454633x^7 + 19195542x^6 + 2085791x^5 - 84556770x^4 - 40115066x^3 + 209940349x^2 + 194016950x - 408451709	\( 101^{9}\cdot 292181^{2} \)	18T913	Trivial (GRH)
18.18.117179983406141848087868879297.1	x^18 - 4x^17 - 36x^16 + 122x^15 + 534x^14 - 1338x^13 - 4276x^12 + 6362x^11 + 19745x^10 - 11530x^9 - 50118x^8 - 3355x^7 + 62559x^6 + 33786x^5 - 26010x^4 - 28933x^3 - 6403x^2 + 1410x + 523	\( 17^{9}\cdot 994046201^{2} \)	18T913	Trivial (GRH)
18.14.6970034779193566051725040347250688.1	x^18 - 114x^16 + 4445x^14 - 67781x^12 + 509956x^10 - 12994356x^8 + 263890063x^6 - 2053193417x^4 + 5773399671x^2 - 3404825447	\( 2^{18}\cdot 23^{9}\cdot 5569^{2}\cdot 21817^{2} \)	18T913	Trivial (GRH)
18.6.9178764557539239451556240651976913.1	x^18 - x^17 - 220x^16 + 192x^15 + 21412x^14 - 16412x^13 - 1210662x^12 + 815812x^11 + 43827399x^10 - 25765391x^9 - 1053188855x^8 + 528345520x^7 + 16789448405x^6 - 6851856807x^5 - 171026989792x^4 + 51244516941x^3 + 1008259194697x^2 - 168842921041x - 2611950958249	\( 97^{9}\cdot 367^{2}\cdot 299401^{2} \)	18T913	Trivial (GRH)