Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (displaying both matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Narrow class group	Unit group torsion	Unit group rank	Regulator
23.1.459...108.1	$x^{23} - 2 x^{22} - x^{21} + 5 x^{20} - x^{19} - 4 x^{18} + 6 x^{15} + 6 x^{14} - 17 x^{13} - 10 x^{12} + 31 x^{11} + 5 x^{10} - 32 x^{9} + 25 x^{7} - 17 x^{5} + 2 x^{4} + 9 x^{3} - 3 x^{2} - 2 x + 1$	$23$	[1,11]	$-\,2^{2}\cdot 1021\cdot 425123\cdot 264472629367076822658099919$	$4$	$35.5239226707$				?	$S_{23}$ (as 23T7)	trivial	trivial	$2$	$11$	$583250036.6$
23.13.291...844.1	$x^{23} - 7 x^{22} + 2 x^{21} + 88 x^{20} - 150 x^{19} - 422 x^{18} + 1148 x^{17} + 862 x^{16} - 4167 x^{15} - 105 x^{14} + 8563 x^{13} - 2935 x^{12} - 10393 x^{11} + 5920 x^{10} + 7285 x^{9} - 5405 x^{8} - 2661 x^{7} + 2503 x^{6} + 354 x^{5} - 537 x^{4} + 19 x^{3} + 39 x^{2} - 3 x - 1$	$23$	[13,5]	$-\,2^{2}\cdot 773\cdot 2479717146827\cdot 380221505923121334124604891$	$4$	$70.19244352$				✓	$S_{23}$ (as 23T7)	trivial	trivial	$2$	$17$	$21282525078200$

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