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 matches 1-50 of 56)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.254891514450553129009.1	x^18 - 5x^17 + 16x^16 - 35x^15 + 59x^14 - 73x^13 + 59x^12 - 5x^11 - 79x^10 + 163x^9 - 224x^8 + 229x^7 - 192x^6 + 127x^5 - 59x^4 + 24x^3 - 4x - 1	\( 7^{12}\cdot 97^{2}\cdot 1399^{2} \)	18T838	Trivial
18.6.2059828821955993600561.1	x^18 - 4x^17 - 2x^16 + 31x^15 - 31x^14 - 82x^13 + 171x^12 + 45x^11 - 353x^10 + 171x^9 + 311x^8 - 328x^7 - 49x^6 + 200x^5 - 85x^4 - 22x^3 + 39x^2 - 11x - 1	\( 7^{12}\cdot 41^{2}\cdot 97^{4} \)	18T838	Trivial (GRH)
18.2.7101528447669869215744.3	x^18 - 3x^16 + 5x^14 - x^12 - 7x^10 + x^8 + 13x^6 - 2x^4 - 5x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 1399^{2} \)	18T838	Trivial (GRH)
18.6.57388858189268996325376.2	x^18 - 2x^16 - 2x^14 - 6x^12 - 10x^10 + 19x^8 + 36x^6 + 3x^4 - 11x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T838	Trivial (GRH)
18.2.57388858189268996325376.3	x^18 + 5x^16 + 8x^14 + 5x^12 + 5x^10 + 19x^8 + 25x^6 + 7x^4 - 3x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T838	Trivial (GRH)
18.6.57388858189268996325376.3	x^18 - 3x^16 - x^14 + 8x^12 - 10x^10 + 14x^8 - 10x^6 + 3x^4 - 2x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T838	Trivial (GRH)
18.2.57388858189268996325376.4	x^18 - x^16 - 4x^14 + 8x^12 + 2x^10 - 18x^8 + 8x^6 + 12x^4 - 8x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T838	Trivial (GRH)
18.6.57388858189268996325376.4	x^18 - 2x^16 - 6x^14 - 2x^12 - 2x^10 + 5x^8 + 18x^6 + 14x^4 + 4x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T838	Trivial (GRH)
18.2.57388858189268996325376.5	x^18 + 9x^16 + 34x^14 + 73x^12 + 101x^10 + 106x^8 + 73x^6 + 23x^4 - 1	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T838	Trivial (GRH)
18.2.57388858189268996325376.6	x^18 - 3x^14 + x^12 - 4x^10 - 2x^8 + 11x^6 + x^4 - 5x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T838	Trivial (GRH)
18.10.66983486784702356675569.2	x^18 - 6x^16 - 4x^15 - 12x^14 - 10x^13 + 111x^12 + 194x^11 - 28x^10 - 377x^9 - 412x^8 - 17x^7 + 333x^6 + 281x^5 + 54x^4 - 53x^3 - 28x^2 + x + 1	\( 7^{12}\cdot 97^{2}\cdot 22679^{2} \)	18T838	Trivial (GRH)
18.10.66983486784702356675569.3	x^18 - 3x^17 + 3x^16 - 18x^14 + 37x^13 - 27x^12 - 12x^11 + 107x^10 - 158x^9 - 7x^8 + 207x^7 - 134x^6 - 64x^5 + 90x^4 - 10x^3 - 16x^2 + 2x + 1	\( 7^{12}\cdot 97^{2}\cdot 22679^{2} \)	18T838	Trivial (GRH)
18.6.2481624923575295556989329.1	x^18 - 3x^17 - 3x^16 + 23x^15 - 19x^14 - 14x^13 + 45x^12 - 46x^11 + 110x^10 - 45x^9 + 268x^8 - 200x^7 - 45x^6 + 77x^5 - 86x^4 + 86x^3 + 3x^2 - 24x - 1	\( 7^{12}\cdot 97^{2}\cdot 138041^{2} \)	18T838	Trivial (GRH)
18.10.2481624923575295556989329.2	x^18 - 2x^17 - 13x^16 + 31x^15 + 46x^14 - 151x^13 - 7x^12 + 234x^11 - 100x^10 - 24x^9 - 141x^8 + 83x^7 + 163x^6 - 91x^5 - 61x^4 + 14x^3 + 22x^2 - 4x - 1	\( 7^{12}\cdot 97^{2}\cdot 138041^{2} \)	18T838	Trivial (GRH)
18.6.2481624923575295556989329.2	x^18 - 9x^17 + 36x^16 - 84x^15 + 98x^14 + 70x^13 - 562x^12 + 1292x^11 - 1813x^10 + 1607x^9 - 625x^8 - 548x^7 + 1208x^6 - 1152x^5 + 711x^4 - 300x^3 + 84x^2 - 14x + 1	\( 7^{12}\cdot 97^{2}\cdot 138041^{2} \)	18T838	Trivial (GRH)
18.10.2481624923575295556989329.3	x^18 - x^17 - 7x^16 + 21x^15 - 4x^14 - 74x^13 + 150x^12 - 17x^11 - 309x^10 + 294x^9 + 39x^8 - 282x^7 + 345x^6 - 26x^5 - 211x^4 + 130x^3 - 30x^2 - 45x + 27	\( 7^{12}\cdot 97^{2}\cdot 138041^{2} \)	18T838	Trivial (GRH)
18.6.3462572249708025242543041.1	x^18 - 4x^17 - 6x^16 + 37x^15 - 17x^14 - 31x^13 + 56x^12 - 305x^11 + 417x^10 - 30x^9 - 1493x^8 + 2568x^7 + 880x^6 - 2743x^5 + 1703x^4 - 755x^3 - 1332x^2 - 108x - 27	\( 7^{12}\cdot 41^{4}\cdot 97^{4} \)	18T838	Trivial (GRH)
18.10.10145719923049728269615104.1	x^18 - 4x^16 - 5x^14 + 28x^12 - 36x^10 + 17x^8 + 17x^6 - 26x^4 + 10x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T838	Trivial (GRH)
18.10.10145719923049728269615104.2	x^18 - 10x^16 + 28x^14 - 22x^12 - 30x^10 + 94x^8 - 78x^6 - 4x^4 + 9x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T838	Trivial (GRH)
18.2.10145719923049728269615104.2	x^18 + 15x^16 + 84x^14 + 231x^12 + 328x^10 + 211x^8 + 9x^6 - 50x^4 - 17x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T838	Trivial (GRH)
18.2.10145719923049728269615104.3	x^18 + 8x^16 + 17x^14 - 12x^12 - 87x^10 - 121x^8 - 88x^6 - 43x^4 - 11x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T838	Trivial (GRH)
18.6.10145719923049728269615104.3	x^18 - 20x^14 - 24x^12 + 82x^10 + 159x^8 + 37x^6 - 40x^4 - 13x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T838	Trivial (GRH)
18.2.10145719923049728269615104.4	x^18 + 14x^16 + 78x^14 + 219x^12 + 313x^10 + 174x^8 - 58x^6 - 97x^4 - 26x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T838	Trivial (GRH)
18.6.10145719923049728269615104.4	x^18 + 4x^16 + 5x^14 - 3x^12 - 38x^10 - 13x^8 + 35x^6 + 12x^4 - 3x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T838	Trivial (GRH)
18.6.10145719923049728269615104.5	x^18 + 4x^16 - 8x^14 - 12x^12 + 16x^10 - 32x^8 - 4x^6 + 38x^4 - x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T838	Trivial (GRH)
18.6.10145719923049728269615104.6	x^18 - 2x^16 - 5x^14 + 12x^12 + 3x^10 - 19x^8 + 7x^6 + 7x^4 - 2x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T838	Trivial (GRH)
18.6.10145719923049728269615104.7	x^18 + 5x^16 - 3x^14 - 20x^12 - 38x^10 + 16x^8 + 85x^6 + 49x^4 + 3x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T838	Trivial (GRH)
18.6.10145719923049728269615104.8	x^18 + x^16 - 3x^14 + 25x^12 - 45x^10 - 100x^8 - 16x^6 + 22x^4 + 3x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52879^{2} \)	18T838	Trivial (GRH)
18.2.10161075065555921079107584.2	x^18 + 14x^16 + 76x^14 + 200x^12 + 257x^10 + 128x^8 - 38x^6 - 96x^4 - 50x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 52919^{2} \)	18T838	Trivial (GRH)
18.6.66818281164125799450935296.1	x^18 - 12x^16 + 67x^14 - 207x^12 + 315x^10 - 1341x^8 + 741x^6 + 2598x^4 + 23474x^2 - 9409	\( 2^{18}\cdot 7^{12}\cdot 97^{2}\cdot 1399^{2} \)	18T838	Trivial (GRH)
18.6.66818281164125799450935296.2	x^18 + 3x^16 - 30x^14 - 85x^12 + 409x^10 + 783x^8 - 3259x^6 - 2065x^4 + 13483x^2 - 9409	\( 2^{18}\cdot 7^{12}\cdot 97^{2}\cdot 1399^{2} \)	18T838	Trivial (GRH)
18.14.69140512696962724890148864.1	x^18 - 9x^16 + 25x^14 - 11x^12 - 50x^10 + 57x^8 + 13x^6 - 36x^4 + 12x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 138041^{2} \)	18T838	Trivial (GRH)
18.10.96470670616161182822957056.1	x^18 - 20x^16 + 145x^14 - 522x^12 + 1181x^10 - 2595x^8 + 5764x^6 - 8301x^4 + 6027x^2 - 1681	\( 2^{18}\cdot 7^{12}\cdot 41^{4}\cdot 97^{2} \)	18T838	Trivial (GRH)
18.6.96470670616161182822957056.1	x^18 + 9x^16 + 22x^14 - 29x^12 - 328x^10 - 498x^8 + 1105x^6 + 750x^4 + 410x^2 - 1681	\( 2^{18}\cdot 7^{12}\cdot 41^{4}\cdot 97^{2} \)	18T838	Trivial (GRH)
18.10.96470670616161182822957056.2	x^18 - 20x^16 + 185x^14 - 951x^12 + 2682x^10 - 4004x^8 + 3931x^6 - 4663x^4 + 4633x^2 - 1681	\( 2^{18}\cdot 7^{12}\cdot 41^{4}\cdot 97^{2} \)	18T838	Trivial (GRH)
18.10.104192253035948620552339456.1	x^18 - 28x^14 + 15x^12 + 168x^10 - 231x^8 + 5x^6 + 63x^4 + 7x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T838	Trivial (GRH)
18.2.104192253035948620552339456.1	x^18 + 14x^16 + 70x^14 + 148x^12 + 84x^10 - 154x^8 - 254x^6 - 126x^4 - 21x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T838	$[2]$ (GRH)
18.6.104192253035948620552339456.1	x^18 + 5x^16 - 16x^14 - 83x^12 - 17x^10 + 215x^8 + 232x^6 + 52x^4 - 11x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T838	Trivial (GRH)
18.10.104192253035948620552339456.2	x^18 - 9x^16 + 17x^14 + 48x^12 - 163x^10 + 40x^8 + 136x^6 + 14x^4 - 12x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T838	Trivial (GRH)
18.14.104192253035948620552339456.2	x^18 - 4x^16 - 16x^14 + 69x^12 + 3x^10 - 232x^8 + 290x^6 - 133x^4 + 22x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T838	Trivial (GRH)
18.2.104192253035948620552339456.2	x^18 + 14x^16 + 69x^14 + 144x^12 + 96x^10 - 82x^8 - 150x^6 - 75x^4 - 15x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T838	$[6]$ (GRH)
18.6.104192253035948620552339456.2	x^18 + 4x^16 - 22x^14 - 125x^12 - 143x^10 + 35x^8 + 88x^6 + 3x^4 - 9x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 169457^{2} \)	18T838	Trivial (GRH)
18.18.584519553822414728713847701504.1	x^18 - 22x^16 + 204x^14 - 1040x^12 + 3188x^10 - 6032x^8 + 6943x^6 - 4582x^4 + 1508x^2 - 169	\( 2^{18}\cdot 7^{12}\cdot 13^{2}\cdot 41^{2}\cdot 23813^{2} \)	18T838	Trivial (GRH)
18.10.699992040933789573282164637696.1	x^18 - 156x^14 + 751x^12 + 402x^10 - 5988x^8 + 3259x^6 + 9882x^4 - 3723x^2 - 5329	\( 2^{18}\cdot 3^{24}\cdot 73^{4}\cdot 577^{2} \)	18T838	Trivial (GRH)
18.14.699992040933789573282164637696.1	x^18 - 15x^16 + 3x^14 + 735x^12 - 2364x^10 - 4677x^8 + 31188x^6 - 49299x^4 + 29784x^2 - 5329	\( 2^{18}\cdot 3^{24}\cdot 73^{4}\cdot 577^{2} \)	18T838	Trivial (GRH)
18.6.699992040933789573282164637696.1	x^18 + 21x^16 + 132x^14 + 118x^12 - 1536x^10 - 4569x^8 + 106x^6 + 12585x^4 + 7884x^2 - 5329	\( 2^{18}\cdot 3^{24}\cdot 73^{4}\cdot 577^{2} \)	18T838	Trivial (GRH)
18.10.699992040933789573282164637696.2	x^18 - 15x^16 - 150x^14 + 963x^12 + 2199x^10 - 11502x^8 - 4453x^6 + 34296x^4 - 13797x^2 - 5329	\( 2^{18}\cdot 3^{24}\cdot 73^{4}\cdot 577^{2} \)	18T838	Trivial (GRH)
18.14.699992040933789573282164637696.2	x^18 - 39x^16 + 576x^14 - 3969x^12 + 11379x^10 + 4122x^8 - 88552x^6 + 128334x^4 + 7008x^2 - 5329	\( 2^{18}\cdot 3^{24}\cdot 73^{4}\cdot 577^{2} \)	18T838	Trivial (GRH)
18.6.699992040933789573282164637696.2	x^18 + 3x^16 - 102x^14 - 419x^12 + 2061x^10 + 9921x^8 - 1757x^6 - 42021x^4 - 40515x^2 - 5329	\( 2^{18}\cdot 3^{24}\cdot 73^{4}\cdot 577^{2} \)	18T838	Trivial (GRH)
18.18.43731966634649207889521071620096.1	x^18 - 78x^16 + 2259x^14 - 32259x^12 + 246870x^10 - 1022352x^8 + 2250359x^6 - 2602659x^4 + 1490391x^2 - 332929	\( 2^{18}\cdot 3^{24}\cdot 73^{2}\cdot 577^{4} \)	18T838	Trivial (GRH)