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 10 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.37586838297210701323.1	x^18 + x^16 - 6x^15 - 5x^13 + 14x^12 + 9x^10 - 17x^9 - 8x^7 + 13x^6 + 4x^4 - 5x^3 - x + 1	\( -\,11\cdot 457\cdot 2339\cdot 14731^{3} \)	18T962	Trivial
18.2.104154322323664273408.1	x^18 + 2x^16 - 6x^15 + 2x^14 - 10x^13 + 15x^12 - 8x^11 + 19x^10 - 20x^9 + 10x^8 - 18x^7 + 14x^6 - 6x^5 + 9x^4 - 6x^3 + 2x^2 - 2x + 1	\( 2^{18}\cdot 11\cdot 43\cdot 587^{3}\cdot 4153 \)	18T962	Trivial
18.4.153308366766150516736.1	x^18 - 6x^17 + 17x^16 - 34x^15 + 57x^14 - 86x^13 + 121x^12 - 148x^11 + 136x^10 - 72x^9 - 7x^8 + 34x^7 + 13x^6 - 76x^5 + 94x^4 - 64x^3 + 24x^2 - 4x - 1	\( -\,2^{18}\cdot 353\cdot 587^{3}\cdot 8191 \)	18T962	Trivial
18.6.19506352827180543375833.1	x^18 - 3x^17 + 2x^16 + 6x^15 - 16x^14 + 11x^13 + 14x^12 - 32x^11 + 15x^10 + 20x^9 - 31x^8 + 8x^7 + 15x^6 - 15x^5 + 2x^4 + 6x^3 - 3x^2 + 1	\( 353^{3}\cdot 379^{3}\cdot 8145811 \)	18T962	Trivial
18.8.28598532373693453982147.1	x^18 - 12x^16 - 6x^15 + 58x^14 + 60x^13 - 127x^12 - 232x^11 + 60x^10 + 406x^9 + 241x^8 - 240x^7 - 388x^6 - 125x^5 + 120x^4 + 136x^3 + 58x^2 + 12x + 1	\( -\,197^{3}\cdot 397\cdot 479^{3}\cdot 85733 \)	18T962	Trivial
18.12.38581896350900372123876643.1	x^18 - 12x^16 - 6x^15 + 54x^14 + 60x^13 - 97x^12 - 216x^11 - 16x^10 + 316x^9 + 293x^8 - 88x^7 - 324x^6 - 185x^5 + 44x^4 + 106x^3 + 54x^2 + 12x + 1	\( -\,3^{3}\cdot 113933\cdot 2323397^{3} \)	18T962	Trivial (GRH)
18.10.77946290565619181652813725.1	x^18 - 17x^16 - 6x^15 + 118x^14 + 85x^13 - 414x^12 - 472x^11 + 693x^10 + 1267x^9 - 202x^8 - 1556x^7 - 881x^6 + 438x^5 + 778x^4 + 423x^3 + 118x^2 + 17x + 1	\( 5^{2}\cdot 92779^{3}\cdot 3903969191 \)	18T962	Trivial (GRH)
18.14.13337661824627376736885669597.1	x^18 - 17x^16 - 6x^15 + 115x^14 + 85x^13 - 379x^12 - 460x^11 + 546x^10 + 1162x^9 + 41x^8 - 1262x^7 - 940x^6 + 189x^5 + 631x^4 + 388x^3 + 115x^2 + 17x + 1	\( 53\cdot 599\cdot 592661^{3}\cdot 2018171 \)	18T962	Trivial (GRH)
18.18.325155846144919090335445159829.1	x^18 - 23x^16 - 6x^15 + 215x^14 + 115x^13 - 1029x^12 - 860x^11 + 2543x^10 + 3112x^9 - 2524x^8 - 5316x^7 - 998x^6 + 2954x^5 + 2658x^4 + 1038x^3 + 215x^2 + 23x + 1	\( 179\cdot 439\cdot 997\cdot 19937\cdot 592661^{3} \)	18T962	Trivial (GRH)
18.16.409666032821894048413630669979.1	x^18 - 18x^16 - 6x^15 + 129x^14 + 90x^13 - 451x^12 - 516x^11 + 699x^10 + 1378x^9 - 19x^8 - 1578x^7 - 1138x^6 + 277x^5 + 789x^4 + 460x^3 + 129x^2 + 18x + 1	\( -\,23\cdot 79^{3}\cdot 3391\cdot 15227^{3}\cdot 3017519 \)	18T962	Trivial (GRH)