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 8 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.3.6826740523487474380439552.1	x^21 - 2x^20 - x^19 - 3x^18 + 10x^17 + 13x^16 + x^15 - 27x^14 - 16x^13 - 20x^12 + 55x^11 - 4x^10 + 8x^9 - 32x^8 - x^7 + 70x^6 - 52x^5 - 4x^4 + 6x^3 + 2x^2 - 6x + 1	\( -\,2^{21}\cdot 71^{10} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)
21.1.156106141952973043121291857.1	x^21 - x^20 - x^19 + 2x^18 + 5x^17 + 2x^16 - 10x^15 - 2x^14 + 23x^13 + 19x^12 - 11x^11 - 28x^10 + 8x^9 + 47x^8 + 23x^7 - 13x^6 - 24x^5 - 7x^4 + 11x^3 + 6x^2 - 1	\( 23^{7}\cdot 71^{9} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)
21.1.1261412107834594448324876441.1	x^21 + 3x^19 - x^18 + x^17 + 8x^16 - 7x^15 + 24x^14 - 15x^13 + 7x^12 + 25x^11 - 42x^10 + 46x^9 - 39x^8 - 12x^7 + 15x^6 - 14x^5 + x^4 + 10x^3 - x^2 + 2x + 1	\( 31^{7}\cdot 71^{9} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)
21.3.822552053520401820057771484375.1	x^21 - 9x^20 + 39x^19 - 110x^18 + 212x^17 - 254x^16 + 72x^15 + 444x^14 - 1230x^13 + 2243x^12 - 3572x^11 + 5129x^10 - 6067x^9 + 5990x^8 - 5448x^7 + 5112x^6 - 4212x^5 + 3001x^4 - 1825x^3 + 903x^2 - 185x + 211	\( -\,5^{9}\cdot 11^{7}\cdot 43^{10} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)
21.7.24136659873181133143007749754988839.1	x^21 - 2x^20 - 7x^19 + 30x^18 + 67x^17 - 166x^16 - 306x^15 + 883x^14 + 1278x^13 - 2134x^12 - 3557x^11 + 2894x^10 + 3853x^9 - 3155x^8 - 310x^7 + 967x^6 + 11x^5 - 146x^4 + 8x^3 + 21x^2 - 1	\( -\,23^{7}\cdot 577^{9} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)
21.7.195035727779935942827580963181007007.1	x^21 + 18x^19 - 20x^18 + 115x^17 - 188x^16 + 227x^15 - 571x^14 - 633x^13 + 412x^12 - 2156x^11 + 1703x^10 + 2628x^9 + 1031x^8 + 1528x^7 - 391x^6 + 241x^5 - 147x^4 + 21x^3 - 10x^2 - x + 1	\( -\,31^{7}\cdot 577^{9} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)
21.21.11025907029010321740711464965433403326464.1	x^21 - x^20 - 49x^19 + 49x^18 + 928x^17 - 894x^16 - 8860x^15 + 7979x^14 + 46924x^13 - 38237x^12 - 141310x^11 + 99810x^10 + 233828x^9 - 134152x^8 - 188281x^7 + 79711x^6 + 52846x^5 - 17134x^4 - 3010x^3 + 526x^2 + 50x - 1	\( 2^{14}\cdot 37^{7}\cdot 577^{9} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)
21.21.234115784066285834308882767309928987624333.1	x^21 - 6x^20 - 37x^19 + 251x^18 + 486x^17 - 4101x^16 - 2503x^15 + 33963x^14 + 600x^13 - 155515x^12 + 45616x^11 + 397419x^10 - 191382x^9 - 530658x^8 + 335989x^7 + 293449x^6 - 253693x^5 - 5734x^4 + 47660x^3 - 14944x^2 + 1819x - 79	\( 229^{7}\cdot 577^{9} \)	$S_3\times D_7$ (as 21T8)	Trivial (GRH)