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 50 matches)

Label	Polynomial	Discriminant	Galois group	Class group
13.3.5570916369223.1	x^13 - x^12 + x^11 - 4x^10 + 5x^9 - 5x^8 + 6x^7 - 2x^6 - 5x^5 + 5x^4 - 7x^3 + 5x^2 - x + 1	\( -\,5570916369223 \)	$S_{13}$ (as 13T9)	Trivial
13.3.5717814639679.1	x^13 - 2x^12 - 3x^11 + 7x^10 + 3x^9 - 7x^8 - 6x^7 + 4x^6 + 8x^5 - 3x^4 - 4x^3 + 2x^2 - 1	\( -\,89\cdot 107\cdot 283\cdot 2121631 \)	$S_{13}$ (as 13T9)	Trivial
13.3.6855574490939.1	x^13 - x^12 + 2x^11 + 2x^10 - 3x^9 + x^8 - x^7 - 8x^6 - 7x^5 - 6x^4 - 6x^3 - 6x^2 - 4x - 1	\( -\,1798333\cdot 3812183 \)	$S_{13}$ (as 13T9)	Trivial
13.3.7805208559959.1	x^13 - 4x^12 + 6x^11 - 6x^10 + 7x^9 - 5x^8 - x^7 + x^6 + 5x^5 - 2x^4 - 3x^3 - x^2 + 1	\( -\,3^{3}\cdot 31\cdot 71\cdot 821\cdot 159977 \)	$S_{13}$ (as 13T9)	Trivial
13.3.9197165262683.1	x^13 - 2x^10 + 2x^9 - x^8 - 3x^7 - 3x^6 + 9x^5 - 10x^4 + 7x^3 + 1	\( -\,82163\cdot 111938041 \)	$S_{13}$ (as 13T9)	Trivial
13.3.14047799762079.1	x^13 - 2x^12 + 2x^10 - 3x^9 + 4x^8 - 4x^7 + 4x^6 - 5x^5 + 3x^4 - 2x^3 + 3x^2 - x - 1	\( -\,3^{3}\cdot 16103\cdot 32310059 \)	$S_{13}$ (as 13T9)	Trivial
13.3.18597951501632.1	x^13 - 2x^12 + x^11 + x^10 - 6x^9 + 3x^8 + 7x^7 - 4x^6 + 4x^4 - 4x^3 - 4x^2 + x + 1	\( -\,2^{6}\cdot 67\cdot 43517\cdot 99667 \)	$S_{13}$ (as 13T9)	Trivial
13.3.21982001088443.1	x^13 - x^12 + x^11 + 3x^10 - 8x^9 + 10x^8 - 6x^7 - 5x^6 + 15x^5 - 19x^4 + 15x^3 - 9x^2 + 3x - 1	\( -\,11^{2}\cdot 71\cdot 2558724373 \)	$S_{13}$ (as 13T9)	Trivial
13.3.21990353102339.1	x^13 - 2x^12 + 4x^11 - 5x^10 + 3x^9 + x^8 - 4x^7 + 9x^6 - 7x^5 + 2x^4 - 4x^2 + 4x - 1	\( -\,157\cdot 3169\cdot 44198783 \)	$S_{13}$ (as 13T9)	Trivial
13.3.34372007159104.1	x^13 - x^12 - 2x^11 + 5x^10 + x^9 - 8x^8 + 5x^7 + 7x^6 - 2x^4 - 4x - 1	\( -\,2^{6}\cdot 29\cdot 239\cdot 77487031 \)	$S_{13}$ (as 13T9)	Trivial
13.3.49047631346319.1	x^13 - 2x^12 + 3x^11 + 2x^10 - 9x^9 + 12x^8 - 2x^7 - 19x^6 + 27x^5 - 19x^4 - x^3 + 11x^2 - 6x + 1	\( -\,3\cdot 16349210448773 \)	$S_{13}$ (as 13T9)	Trivial
13.3.53877019237375.1	x^13 - 2x^12 - 4x^11 + 7x^10 + 6x^9 - 6x^8 - 6x^7 - 8x^6 + 8x^5 + 15x^4 - 7x^3 - 7x^2 + x + 1	\( -\,5^{3}\cdot 204793\cdot 2104643 \)	$S_{13}$ (as 13T9)	Trivial
13.3.60464861374756.1	x^13 - x^11 - 3x^10 - x^9 + 4x^8 + 5x^7 - x^6 - 6x^5 - 5x^4 + x^3 + 4x^2 + 3x + 1	\( -\,2^{2}\cdot 15116215343689 \)	$S_{13}$ (as 13T9)	Trivial
13.3.69188908404875.1	x^13 - 3x^12 + 3x^11 - 3x^10 + 5x^9 + 2x^8 - 17x^7 + 10x^6 + 16x^5 - 16x^4 - 5x^3 + 7x^2 - 1	\( -\,5^{3}\cdot 7^{5}\cdot 31\cdot 1062367 \)	$S_{13}$ (as 13T9)	Trivial
13.3.96082590998375.1	x^13 - 4x^11 - 3x^10 + 9x^9 + 10x^8 - 4x^7 - 12x^6 - 13x^5 + 5x^4 + 12x^3 - x + 1	\( -\,5^{3}\cdot 768660727987 \)	$S_{13}$ (as 13T9)	Trivial
13.3.105628246955776.1	x^13 - x^12 + 3x^11 - x^10 + 3x^9 + 6x^8 - 6x^7 + x^6 + 6x^5 - 8x^4 - 9x^3 + 2x^2 + 4x + 1	\( -\,2^{8}\cdot 257\cdot 1605487703 \)	$S_{13}$ (as 13T9)	Trivial
13.3.114312593686528.1	x^13 - x^12 - 5x^11 + 15x^9 + 9x^8 - 28x^7 - 20x^6 + 26x^5 + 20x^4 - 12x^3 - 10x^2 + 2x + 2	\( -\,2^{14}\cdot 6977087017 \)	$S_{13}$ (as 13T9)	Trivial
13.3.134713017952000.1	x^13 - 5x^12 + 15x^11 - 34x^10 + 56x^9 - 79x^8 + 85x^7 - 78x^6 + 53x^5 - 25x^4 + 6x^3 + 4x^2 - 2x + 1	\( -\,2^{8}\cdot 5^{3}\cdot 4209781811 \)	$S_{13}$ (as 13T9)	Trivial
13.3.156408138976000.1	x^13 - 3x^12 + 3x^11 - 4x^10 + 4x^9 + 7x^8 - 20x^7 + 27x^6 - 35x^5 + 41x^4 - 36x^3 + 24x^2 - 12x + 4	\( -\,2^{8}\cdot 5^{3}\cdot 137\cdot 599\cdot 59561 \)	$S_{13}$ (as 13T9)	Trivial
13.3.215762905145828.1	x^13 - 2x^12 + x^11 + 5x^10 - 10x^9 + 4x^8 + 8x^7 - 13x^6 + 5x^5 + 10x^4 - 9x^3 - 3x^2 + 4x + 1	\( -\,2^{2}\cdot 953\cdot 10313\cdot 5488313 \)	$S_{13}$ (as 13T9)	Trivial
13.3.509211272757248.1	x^13 - x^12 - 2x^11 - 2x^10 + 3x^9 + 4x^8 + 8x^7 - 4x^6 - 13x^5 + 3x^4 + 2x^3 - 6x^2 + x + 2	\( -\,2^{14}\cdot 31079789597 \)	$S_{13}$ (as 13T9)	Trivial
13.3.1990387975424000.1	x^13 - x^12 - 4x^11 - 2x^10 + 6x^9 + 3x^8 - x^7 - 6x^6 + x^4 + x^3 - 12x^2 - 3x + 1	\( -\,2^{11}\cdot 5^{3}\cdot 84089\cdot 92461 \)	$S_{13}$ (as 13T9)	Trivial
13.3.71106764206294000.1	x^13 - 2x^12 - x^11 + 4x^10 + 4x^9 + 5x^8 - 27x^7 - 6x^6 - 16x^5 + 80x^4 + 27x^3 - 13x^2 - 84x - 36	\( -\,2^{4}\cdot 5^{3}\cdot 241\cdot 147524407067 \)	$S_{13}$ (as 13T9)	Trivial
13.3.14214841139858258435.1	x^13 - 3x - 1	\( -\,5\cdot 226169\cdot 12570105664223 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.597108795955749072896.1	x^13 - 4x - 2	\( -\,2^{12}\cdot 11546071\cdot 12625811381 \)	$S_{13}$ (as 13T9)	Trivial
13.3.598349069517244348931.1	x^13 - 4x - 1	\( -\,23\cdot 17579\cdot 1479900843934943 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.1195458168348100014080.1	x^13 - 8x - 4	\( -\,2^{12}\cdot 5\cdot 23\cdot 1993\cdot 1273413051689 \)	$S_{13}$ (as 13T9)	Trivial
13.3.2373255092266725781827.1	x^13 - 6x - 3	\( -\,3^{12}\cdot 24749\cdot 180439539103 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.5531848059151973728256.1	x^13 - 9x - 4	\( -\,2^{14}\cdot 43\cdot 7852028154455813 \)	$S_{13}$ (as 13T9)	Trivial
13.3.10722951430477506473427.1	x^13 - 5x - 3	\( -\,3^{12}\cdot 37\cdot 1033\cdot 527906776207 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.10882671103563398131712.1	x^13 - 5x - 2	\( -\,2^{12}\cdot 1373\cdot 4079\cdot 93893\cdot 5052637 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.10883911377124893407747.1	x^13 - 5x - 1	\( -\,97\cdot 7489\cdot 14982677517575459 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.27842264671567701082112.1	x^13 - 6x - 4	\( -\,2^{22}\cdot 7\cdot 11\cdot 86209262103439 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.95967909874601161719291.1	x^13 - 7x - 3	\( -\,3^{11}\cdot 71\cdot 8627573\cdot 884392891 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.116449219194155454967808.1	x^13 - 6x - 2	\( -\,2^{12}\cdot 7\cdot 29\cdot 1601\cdot 10211\cdot 8566846531 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.116450459467716950243843.1	x^13 - 6x - 1	\( -\,7\cdot 106123\cdot 474647\cdot 330265270729 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.196067122333410552143483.1	x^13 - 8x - 1	\( -\,196067122333410552143483 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.215967727136124086782976.1	x^13 - 7x - 2	\( -\,2^{10}\cdot 6311\cdot 33418789974864709 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.789928031300558681422067.1	x^13 - 7x - 5	\( -\,11\cdot 6389\cdot 11239887182523352373 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.858790748036611696492544.1	x^13 - 7x - 4	\( -\,2^{25}\cdot 397\cdot 64468409915761 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.863872148818057842407939.1	x^13 - 7x - 1	\( -\,1951\cdot 442784289501823599389 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.4242384876594005425336320.1	x^13 - 8x - 6	\( -\,2^{12}\cdot 3^{12}\cdot 5\cdot 11943947\cdot 32634517 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.4827733940817764642601203.1	x^13 - 8x - 5	\( -\,521\cdot 1231\cdot 7527444318037649653 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.4901517098388616416652755.1	x^13 - 8x - 3	\( -\,3^{12}\cdot 5\cdot 11\cdot 59\cdot 103\cdot 27594564189113 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.4901676818061702308311040.1	x^13 - 8x - 2	\( -\,2^{12}\cdot 5\cdot 239339688381919058023 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.18471349714993943468790371.1	x^13 - 9x - 7	\( -\,1531661\cdot 12059685344860216111 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.22004237869326672158601216.1	x^13 - 9x - 6	\( -\,2^{12}\cdot 3^{12}\cdot 182029\cdot 55532949839 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.22589586933550431375866099.1	x^13 - 9x - 5	\( -\,23\cdot 101\cdot 9724316372600271793313 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.22663370091121283149917651.1	x^13 - 9x - 3	\( -\,3^{12}\cdot 54469\cdot 16734163\cdot 46786013 \)	$S_{13}$ (as 13T9)	Trivial (GRH)
13.3.22663529810794369041575936.1	x^13 - 9x - 2	\( -\,2^{12}\cdot 16519\cdot 334952983395693989 \)	$S_{13}$ (as 13T9)	Trivial (GRH)