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 100)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.2199140361717170013184.1	x^20 - 5x^19 + 11x^18 - 11x^17 - 2x^16 + 16x^15 - 2x^14 - 24x^13 + 22x^12 + 8x^11 - 22x^10 - 13x^9 + 14x^8 + 3x^7 + x^6 + 15x^5 + 20x^4 + 9x^3 + 3x^2 + 2x + 1	\( 2^{10}\cdot 7^{6}\cdot 23^{2}\cdot 431^{4} \)	20T994	Trivial
20.4.12646126110965776516096.1	x^20 - x^18 - 4x^16 + 4x^14 + 9x^12 - 11x^10 - 9x^8 + 12x^6 + x^4 - 4x^2 + 1	\( 2^{10}\cdot 47^{2}\cdot 8647^{4} \)	20T994	Trivial (GRH)
20.0.13656348922320778494976.1	x^20 - 4x^19 + 2x^18 + 12x^17 - 24x^16 + 16x^15 + 4x^14 - 5x^13 + x^12 - 58x^11 + 188x^10 - 272x^9 + 227x^8 - 163x^7 + 197x^6 - 254x^5 + 212x^4 - 105x^3 + 31x^2 - 6x + 1	\( 2^{10}\cdot 17^{6}\cdot 79^{2}\cdot 97^{4} \)	20T994	Trivial (GRH)
20.0.34658380663301814682624.1	x^20 - 5x^18 + 14x^16 - 26x^14 + 34x^12 - 32x^10 + 23x^8 - 13x^6 + 8x^4 - 4x^2 + 1	\( 2^{10}\cdot 191^{2}\cdot 5519^{4} \)	20T994	Trivial (GRH)
20.0.156746706211961203326976.3	x^20 - 4x^18 + 6x^16 - 4x^14 + 3x^12 - 5x^10 + 6x^8 - 6x^6 + 7x^4 - 4x^2 + 1	\( 2^{20}\cdot 13^{4}\cdot 19^{2}\cdot 347^{4} \)	20T994	Trivial (GRH)
20.4.289274162775135942344704.1	x^20 - 2x^19 + 6x^17 - 9x^16 - x^15 + 16x^14 - 9x^13 - 20x^12 + 36x^11 - 8x^10 - 38x^9 + 48x^8 - 13x^7 - 20x^6 + 13x^5 + 16x^4 - 29x^3 + 20x^2 - 7x + 1	\( 2^{18}\cdot 32411^{4} \)	20T994	Trivial (GRH)
20.0.670930019119154175410176.1	x^20 + x^16 - x^14 - 4x^12 + 7x^10 - 6x^8 + 11x^6 - 17x^4 + 8x^2 + 1	\( 2^{20}\cdot 7^{4}\cdot 41^{2}\cdot 631^{4} \)	20T994	Trivial (GRH)
20.4.670930019119154175410176.2	x^20 + x^16 + x^14 - 4x^12 - 7x^10 - 6x^8 - 11x^6 - 17x^4 - 8x^2 + 1	\( 2^{20}\cdot 7^{4}\cdot 41^{2}\cdot 631^{4} \)	20T994	Trivial (GRH)
20.0.673757209047664342073344.1	x^20 - 2x^16 + x^14 - x^12 - x^10 + 3x^8 + 2x^6 - 2x^4 - x^2 + 1	\( 2^{20}\cdot 53^{2}\cdot 3889^{4} \)	20T994	Trivial (GRH)
20.4.673757209047664342073344.2	x^20 - 2x^16 - x^14 - x^12 + x^10 + 3x^8 - 2x^6 - 2x^4 + x^2 + 1	\( 2^{20}\cdot 53^{2}\cdot 3889^{4} \)	20T994	Trivial (GRH)
20.4.726016314793265336172544.1	x^20 - 2x^18 - 4x^16 + 30x^14 - 61x^12 + 52x^10 - 9x^8 - 23x^6 + 33x^4 - 20x^2 + 4	\( 2^{14}\cdot 83^{4}\cdot 983^{4} \)	20T994	Trivial (GRH)
20.4.726016314793265336172544.2	x^20 + 5x^18 + 12x^16 + 22x^14 + 15x^12 - 8x^10 - 35x^8 - 29x^6 + 4x^4 + 4x^2 + 1	\( 2^{14}\cdot 83^{4}\cdot 983^{4} \)	20T994	Trivial (GRH)
20.0.829565981540845553188864.2	x^20 + x^18 - 4x^16 - 5x^14 + 5x^12 + 12x^10 + 17x^8 + 17x^6 + 9x^4 + 5x^2 + 1	\( 2^{20}\cdot 37^{2}\cdot 4903^{4} \)	20T994	Trivial (GRH)
20.0.829565981540845553188864.3	x^20 + 4x^18 + 9x^16 + 15x^14 + 17x^12 + 11x^10 - 2x^8 - 4x^6 + 3x^4 + 4x^2 + 1	\( 2^{20}\cdot 37^{2}\cdot 4903^{4} \)	20T994	Trivial (GRH)
20.4.829565981540845553188864.5	x^20 - x^18 - 4x^16 + 5x^14 + 5x^12 - 12x^10 + 17x^8 - 17x^6 + 9x^4 - 5x^2 + 1	\( 2^{20}\cdot 37^{2}\cdot 4903^{4} \)	20T994	Trivial (GRH)
20.4.829565981540845553188864.6	x^20 - 4x^18 + 9x^16 - 15x^14 + 17x^12 - 11x^10 - 2x^8 + 4x^6 + 3x^4 - 4x^2 + 1	\( 2^{20}\cdot 37^{2}\cdot 4903^{4} \)	20T994	Trivial (GRH)
20.4.882316447948636312484929.1	x^20 - 5x^19 + 4x^18 + 21x^17 - 43x^16 - 28x^15 + 159x^14 - 91x^13 - 265x^12 + 491x^11 - 199x^10 - 295x^9 + 401x^8 - 113x^7 - 118x^6 + 109x^5 - 25x^4 - 7x^3 + 6x^2 - 3x + 1	\( 7^{6}\cdot 43^{4}\cdot 1217^{4} \)	20T994	Trivial (GRH)
20.8.882316447948636312484929.1	x^20 - 4x^19 + 6x^18 - 4x^17 - 9x^16 + 35x^15 - 49x^14 + 25x^13 + 31x^12 - 93x^11 + 108x^10 - 17x^9 - 39x^8 + 9x^7 - 11x^6 + 8x^5 - 69x^4 + 80x^3 - 4x^2 - 4x - 1	\( 7^{6}\cdot 43^{4}\cdot 1217^{4} \)	20T994	Trivial (GRH)
20.8.1860495326773308902342656.1	x^20 - 4x^18 - 2x^17 + x^16 + 28x^15 - 23x^14 - 32x^13 + 46x^12 - 54x^11 + 112x^10 - 72x^9 - 68x^8 + 94x^7 - 27x^6 + 26x^5 - 45x^4 + 18x^3 + 7x^2 - 6x + 1	\( 2^{20}\cdot 36497^{4} \)	20T994	Trivial (GRH)
20.8.2320349626175642005405696.1	x^20 - 10x^19 + 45x^18 - 120x^17 + 209x^16 - 244x^15 + 182x^14 - 64x^13 - 38x^12 + 124x^11 - 222x^10 + 268x^9 - 171x^8 - 22x^7 + 137x^6 - 100x^5 + 13x^4 + 24x^3 - 12x^2 + 1	\( 2^{20}\cdot 38569^{4} \)	20T994	Trivial (GRH)
20.4.7170151093155466780795369.2	x^20 - 4x^19 + 8x^18 - 15x^17 + 5x^16 + 2x^15 - 54x^14 + 87x^13 - 68x^12 + 11x^11 + 205x^10 - 394x^9 + 580x^8 - 643x^7 + 554x^6 - 410x^5 + 231x^4 - 109x^3 + 37x^2 - 9x + 1	\( 53^{6}\cdot 4241^{4} \)	20T994	Trivial (GRH)
20.0.10751439513964248879333376.1	x^20 + 6x^18 + 18x^16 + 40x^14 + 64x^12 + 64x^10 + 34x^8 + x^6 - 4x^4 + 4x^2 + 1	\( 2^{20}\cdot 53^{4}\cdot 59^{2}\cdot 139^{4} \)	20T994	Trivial (GRH)
20.8.10751439513964248879333376.1	x^20 - 6x^18 + 18x^16 - 40x^14 + 64x^12 - 64x^10 + 34x^8 - x^6 - 4x^4 - 4x^2 + 1	\( 2^{20}\cdot 53^{4}\cdot 59^{2}\cdot 139^{4} \)	20T994	Trivial (GRH)
20.0.12441912188918164240728064.1	x^20 + 6x^18 + 20x^16 + 40x^14 + 57x^12 + 73x^10 + 71x^8 + 46x^6 + 24x^4 + 8x^2 + 1	\( 2^{20}\cdot 103^{2}\cdot 5783^{4} \)	20T994	Trivial (GRH)
20.8.30022900559553681267097600.2	x^20 - 4x^19 + 30x^17 - 71x^16 + 58x^15 + 13x^14 - 78x^13 + 302x^12 - 1060x^11 + 2110x^10 - 2276x^9 + 800x^8 + 1370x^7 - 2545x^6 + 2190x^5 - 1149x^4 + 360x^3 - 51x^2 - 2x + 1	\( 2^{30}\cdot 5^{2}\cdot 5783^{4} \)	20T994	Trivial (GRH)
20.4.37518831457268229509332441.1	x^20 - 4x^19 + 7x^18 - 11x^17 + 14x^16 - 11x^15 + 4x^14 + x^13 - 9x^12 + 25x^11 - 9x^10 + 25x^9 - 9x^8 + x^7 + 4x^6 - 11x^5 + 14x^4 - 11x^3 + 7x^2 - 4x + 1	\( 11^{4}\cdot 19^{4}\cdot 199^{4}\cdot 3541^{2} \)	20T994	Trivial (GRH)
20.0.185860176587075926060171264.1	x^20 + 5x^18 + 6x^16 + 19x^14 + 64x^12 + 92x^10 + 79x^8 + 46x^6 + 23x^4 + 8x^2 + 1	\( 2^{22}\cdot 83^{4}\cdot 983^{4} \)	20T994	$[2]$ (GRH)
20.8.185860176587075926060171264.1	x^20 - 7x^18 + 20x^16 - 35x^14 + 56x^12 - 75x^10 + 42x^8 + 14x^6 - 11x^4 - 8x^2 + 4	\( 2^{22}\cdot 83^{4}\cdot 983^{4} \)	20T994	Trivial (GRH)
20.0.185860176587075926060171264.2	x^20 + 7x^18 + 20x^16 + 35x^14 + 56x^12 + 75x^10 + 42x^8 - 14x^6 - 11x^4 + 8x^2 + 4	\( 2^{22}\cdot 83^{4}\cdot 983^{4} \)	20T994	$[2]$ (GRH)
20.8.185860176587075926060171264.2	x^20 - 5x^18 + 6x^16 - 19x^14 + 64x^12 - 92x^10 + 79x^8 - 46x^6 + 23x^4 - 8x^2 + 1	\( 2^{22}\cdot 83^{4}\cdot 983^{4} \)	20T994	Trivial (GRH)
20.4.234469216752693654699638784.1	x^20 - 10x^19 + 49x^18 - 152x^17 + 321x^16 - 466x^15 + 437x^14 - 198x^13 - 73x^12 + 204x^11 - 252x^10 + 298x^9 - 259x^8 + 160x^7 - 119x^6 + 92x^5 - 29x^4 + 16x^3 - 10x^2 - 1	\( 2^{20}\cdot 3^{2}\cdot 17^{4}\cdot 4153^{4} \)	20T994	Trivial (GRH)
20.8.234469216752693654699638784.1	x^20 - 4x^19 - 4x^18 + 28x^17 - 10x^16 - 64x^15 + 68x^14 + 58x^13 - 177x^12 + 164x^11 - 121x^10 + 164x^9 - 177x^8 + 58x^7 + 68x^6 - 64x^5 - 10x^4 + 28x^3 - 4x^2 - 4x + 1	\( 2^{20}\cdot 3^{2}\cdot 17^{4}\cdot 4153^{4} \)	20T994	Trivial (GRH)
20.4.234469216752693654699638784.2	x^20 - 6x^19 + 15x^18 - 26x^17 + 82x^16 - 256x^15 + 481x^14 - 626x^13 + 939x^12 - 1722x^11 + 2306x^10 - 1668x^9 + 1646x^7 - 2495x^6 + 2356x^5 - 1605x^4 + 824x^3 - 314x^2 + 78x - 9	\( 2^{20}\cdot 3^{2}\cdot 17^{4}\cdot 4153^{4} \)	20T994	Trivial (GRH)
20.8.234469216752693654699638784.2	x^20 - 3x^18 - 6x^17 - 21x^16 - 24x^15 + 18x^14 + 84x^13 + 6x^12 - 228x^11 - 181x^10 + 142x^9 + 266x^8 + 40x^7 - 240x^6 - 142x^5 + 84x^4 + 62x^3 - 10x^2 - 6x + 1	\( 2^{20}\cdot 3^{2}\cdot 17^{4}\cdot 4153^{4} \)	20T994	Trivial (GRH)
20.4.249238158195972964709564416.1	x^20 + x^18 + 2x^14 - 5x^12 - 48x^10 - 97x^8 - 60x^6 + 4x^4 + 8x^2 + 1	\( 2^{20}\cdot 461^{2}\cdot 5783^{4} \)	20T994	Trivial (GRH)
20.8.249238158195972964709564416.1	x^20 - 9x^18 + 33x^16 - 65x^14 + 78x^12 - 62x^10 + 28x^8 + 6x^6 - 13x^4 + x^2 + 1	\( 2^{20}\cdot 461^{2}\cdot 5783^{4} \)	20T994	Trivial (GRH)
20.0.346253474022222298149289984.1	x^20 + 12x^18 + 63x^16 + 179x^14 + 278x^12 + 205x^10 + 27x^8 - 29x^6 + 6x^4 + 8x^2 + 1	\( 2^{20}\cdot 13^{4}\cdot 19^{2}\cdot 47^{2}\cdot 347^{4} \)	20T994	$[2]$ (GRH)
20.12.346253474022222298149289984.1	x^20 - 12x^18 + 63x^16 - 179x^14 + 278x^12 - 205x^10 + 27x^8 + 29x^6 + 6x^4 - 8x^2 + 1	\( 2^{20}\cdot 13^{4}\cdot 19^{2}\cdot 47^{2}\cdot 347^{4} \)	20T994	Trivial (GRH)
20.0.378737960796861226766181376.1	x^20 + 11x^18 - 10x^17 + 72x^16 - 117x^15 + 344x^14 - 665x^13 + 1347x^12 - 2415x^11 + 3867x^10 - 5816x^9 + 7688x^8 - 9087x^7 + 9123x^6 - 7265x^5 + 4359x^4 - 1726x^3 + 361x^2 - 20x + 1	\( 2^{10}\cdot 17^{2}\cdot 61^{6}\cdot 397^{4} \)	20T994	Trivial (GRH)
20.4.378737960796861226766181376.1	x^20 - 5x^19 + 21x^18 - 66x^17 + 173x^16 - 408x^15 + 835x^14 - 1511x^13 + 2186x^12 - 2662x^11 + 2541x^10 - 1782x^9 + 827x^8 + 303x^7 - 658x^6 + 947x^5 - 516x^4 + 344x^3 - 73x^2 + 37x - 5	\( 2^{10}\cdot 17^{2}\cdot 61^{6}\cdot 397^{4} \)	20T994	Trivial (GRH)
20.4.392139086823683498913562624.1	x^20 + 6x^18 + 10x^16 - 3x^14 - 16x^12 + 2x^10 + 7x^8 - 13x^6 - 2x^4 + 8x^2 + 1	\( 2^{20}\cdot 13^{2}\cdot 38569^{4} \)	20T994	Trivial (GRH)
20.8.392139086823683498913562624.1	x^20 - 4x^18 + x^16 + 13x^14 - 9x^12 - 21x^10 + 16x^8 + 18x^6 - 9x^4 - 6x^2 + 1	\( 2^{20}\cdot 13^{2}\cdot 38569^{4} \)	20T994	Trivial (GRH)
20.8.392139086823683498913562624.2	x^20 - 6x^18 + 10x^16 + 3x^14 - 16x^12 - 2x^10 + 7x^8 + 13x^6 - 2x^4 - 8x^2 + 1	\( 2^{20}\cdot 13^{2}\cdot 38569^{4} \)	20T994	Trivial (GRH)
20.4.458889669961949873970903616.1	x^20 - 5x^18 + 8x^16 + 4x^14 - 16x^12 + 7x^10 - 29x^8 + 27x^6 - 7x^4 + x^2 + 1	\( 2^{6}\cdot 53^{6}\cdot 4241^{4} \)	20T994	Trivial (GRH)
20.0.3434617864486783566285816409.1	x^20 - x^19 - 3x^18 + 6x^17 + x^16 - 7x^15 + 6x^14 - 5x^13 + x^12 - 5x^11 + 13x^10 - 5x^9 + x^8 - 5x^7 + 6x^6 - 7x^5 + x^4 + 6x^3 - 3x^2 - x + 1	\( 7^{2}\cdot 103^{2}\cdot 137^{4}\cdot 163^{6} \)	20T994	Trivial (GRH)
20.4.13083641515520609586402820096.1	x^20 - 2x^19 - 8x^18 + 24x^17 + 11x^16 - 108x^15 + 90x^14 + 206x^13 - 487x^12 + 132x^11 + 826x^10 - 1342x^9 + 878x^8 - 366x^7 + 368x^6 - 260x^5 - 44x^4 + 108x^3 - 32x^2 + 1	\( 2^{30}\cdot 7^{2}\cdot 137^{4}\cdot 163^{4} \)	20T994	Trivial (GRH)
20.12.18992006556968186030670741504.1	x^20 - 6x^19 + 3x^18 + 64x^17 - 178x^16 - 42x^15 + 954x^14 - 1412x^13 - 888x^12 + 4770x^11 - 3562x^10 - 4938x^9 + 9635x^8 - 536x^7 - 10793x^6 + 5156x^5 + 7152x^4 - 4926x^3 - 1740x^2 + 1770x - 311	\( 2^{20}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4} \)	20T994	Trivial (GRH)
20.4.18992006556968186030670741504.2	x^20 - 10x^19 + 55x^18 - 210x^17 + 613x^16 - 1436x^15 + 2778x^14 - 4516x^13 + 6188x^12 - 7072x^11 + 6440x^10 - 4068x^9 + 590x^8 + 2606x^7 - 4173x^6 + 3802x^5 - 2327x^4 + 942x^3 - 225x^2 + 22x + 1	\( 2^{20}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4} \)	20T994	Trivial (GRH)
20.0.23669886536617724097143504896.1	x^20 + 15x^18 + 99x^16 + 378x^14 + 917x^12 + 1449x^10 + 1460x^8 + 876x^6 + 272x^4 + 33x^2 + 1	\( 2^{20}\cdot 101^{2}\cdot 38569^{4} \)	20T994	$[2]$ (GRH)
20.12.23669886536617724097143504896.2	x^20 - 15x^18 + 99x^16 - 378x^14 + 917x^12 - 1449x^10 + 1460x^8 - 876x^6 + 272x^4 - 33x^2 + 1	\( 2^{20}\cdot 101^{2}\cdot 38569^{4} \)	20T994	Trivial (GRH)