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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.8.33882845805158779964647.1	x^18 - 2x^17 - 10x^16 + 26x^15 - 8x^14 - 53x^13 + 95x^12 - 43x^11 - 80x^10 + 147x^9 - 80x^8 - 43x^7 + 95x^6 - 53x^5 - 8x^4 + 26x^3 - 10x^2 - 2x + 1	\( -\,7^{13}\cdot 769^{4} \)	18T552	Trivial
18.8.36491143759213924473147.1	x^18 - 3x^17 - 8x^16 + 26x^15 + 13x^14 - 60x^13 - 20x^12 + 93x^11 + 7x^10 - 99x^9 + 7x^8 + 93x^7 - 20x^6 - 60x^5 + 13x^4 + 26x^3 - 8x^2 - 3x + 1	\( -\,3^{3}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4} \)	18T552	Trivial
18.12.354293866282050926558838784.1	x^18 - 14x^16 + 65x^14 - 127x^12 + 83x^10 + 43x^8 - 59x^6 - 2x^4 + 8x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4} \)	18T552	Trivial (GRH)
18.4.354293866282050926558838784.1	x^18 + 11x^16 + 40x^14 + 36x^12 - 95x^10 - 223x^8 - 137x^6 + 15x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4} \)	18T552	Trivial
18.12.354293866282050926558838784.2	x^18 - x^16 - 37x^14 + 116x^12 + 19x^10 - 352x^8 + 276x^6 - 64x^4 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4} \)	18T552	Trivial (GRH)
18.4.354293866282050926558838784.2	x^18 + 16x^16 + 88x^14 + 193x^12 + 111x^10 - 106x^8 - 92x^6 + 15x^4 + 12x^2 + 1	\( -\,2^{18}\cdot 7^{12}\cdot 13^{4}\cdot 43^{4} \)	18T552	Trivial
18.0.8882184730747543215052423168.1	x^18 + 21x^16 + 179x^14 + 812x^12 + 2138x^10 + 3318x^8 + 2925x^6 + 1323x^4 + 245x^2 + 7	\( -\,2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T552	$[48]$ (GRH)
18.10.8882184730747543215052423168.1	x^18 - 5x^16 - 20x^14 + 81x^12 + 115x^10 - 220x^8 - 204x^6 + 154x^4 + 112x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T552	Trivial (GRH)
18.14.8882184730747543215052423168.1	x^18 - 11x^16 + 34x^14 + 14x^12 - 225x^10 + 311x^8 - 27x^6 - 182x^4 + 91x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T552	Trivial (GRH)
18.18.8882184730747543215052423168.1	x^18 - 21x^16 + 179x^14 - 812x^12 + 2138x^10 - 3318x^8 + 2925x^6 - 1323x^4 + 245x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T552	Trivial (GRH)
18.6.8882184730747543215052423168.1	x^18 - x^16 - 47x^14 + 24x^12 + 502x^10 - 190x^8 - 1086x^6 - 693x^4 - 140x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T552	Trivial (GRH)
18.10.8882184730747543215052423168.2	x^18 - 11x^16 + 4x^14 + 73x^12 - 15x^10 - 135x^8 - 8x^6 + 84x^4 + 21x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T552	Trivial (GRH)
18.14.8882184730747543215052423168.2	x^18 - 20x^16 + 143x^14 - 392x^12 - 16x^10 + 1801x^8 - 1812x^6 - 1561x^4 + 1960x^2 - 343	\( 2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T552	Trivial (GRH)
18.6.8882184730747543215052423168.2	x^18 + 17x^16 + 76x^14 + 14x^12 - 379x^10 - 263x^8 + 484x^6 + 210x^4 - 14x^2 - 7	\( 2^{18}\cdot 7^{13}\cdot 769^{4} \)	18T552	Trivial (GRH)
18.0.62175293115232802505366962176.1	x^18 + 30x^16 + 349x^14 + 2085x^12 + 7021x^10 + 13685x^8 + 15239x^6 + 9016x^4 + 2254x^2 + 49	\( -\,2^{18}\cdot 7^{14}\cdot 769^{4} \)	18T552	$[6, 24]$ (GRH)
18.18.224695650053140671980101468684288.1	x^18 - 70x^16 + 2058x^14 - 33054x^12 + 315462x^10 - 1817410x^8 + 6099030x^6 - 10709832x^4 + 7448245x^2 - 634207	\( 2^{18}\cdot 7^{15}\cdot 13^{4}\cdot 43^{6} \)	18T552	Trivial (GRH)