Number field search results

Results (4 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	Unit signature rank	Max $p$
20.0.625...064.1	$x^{20} - 6 x^{18} + 11 x^{16} + 2 x^{14} - 43 x^{12} + 102 x^{10} - 146 x^{8} + 134 x^{6} - 84 x^{4} + 32 x^{2} + 1$	$20$	(0, 10)	$2^{30}\cdot 17^{12}$	$2$	$15.4815466703$	$18.700114874768015$			?	$A_5$ (as 20T15)	trivial	trivial	$2$	$9$	$13329.0422668$	$0$	$17$
20.0.379...784.1	$x^{20} - 10 x^{19} + 56 x^{18} - 218 x^{17} + 643 x^{16} - 1494 x^{15} + 2800 x^{14} - 4298 x^{13} + 5465 x^{12} - 5814 x^{11} + 5242 x^{10} - 4092 x^{9} + 2856 x^{8} - 1830 x^{7} + 1078 x^{6} - 550 x^{5} + 225 x^{4} - 50 x^{3} + 6 x^{2} - 4 x + 2$	$20$	(0, 10)	$2^{30}\cdot 29^{12}$	$2$	$21.3296530991$	$26.697893241960433$			?	$A_5$ (as 20T15)	trivial	trivial	$2$	$9$	$447869.030966$	$0$	$29$
20.20.285...449.1	$x^{20} - 5 x^{19} - 57 x^{18} + 200 x^{17} + 1122 x^{16} - 2859 x^{15} - 9033 x^{14} + 20641 x^{13} + 28417 x^{12} - 79221 x^{11} - 12858 x^{10} + 134055 x^{9} - 74283 x^{8} - 57223 x^{7} + 73078 x^{6} - 20117 x^{5} - 4435 x^{4} + 2805 x^{3} - 177 x^{2} - 51 x + 1$	$20$	(20, 0)	$19^{10}\cdot 293^{10}$	$2$	$74.6123314205$	$74.61233142048303$			?	$A_5$ (as 20T15)	$[6]$	$[2, 2, 6]$	$2$	$19$	$586413993994$	$18$	$293$
20.20.336...625.1	$x^{20} - 10 x^{19} - 15 x^{18} + 355 x^{17} - 85 x^{16} - 5333 x^{15} + 2720 x^{14} + 43940 x^{13} - 16315 x^{12} - 212780 x^{11} + 16401 x^{10} + 594910 x^{9} + 152230 x^{8} - 860395 x^{7} - 495745 x^{6} + 452545 x^{5} + 436755 x^{4} + 69475 x^{3} - 18175 x^{2} - 4575 x - 115$	$20$	(20, 0)	$5^{26}\cdot 41^{12}$	$2$	$75.2196519688$	$96.34967264566555$			?	$A_5$ (as 20T15)	$[2]$	$[2, 2, 4]$	$2$	$19$	$1908142429540$	$17$	$41$

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