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 235)

Label	Polynomial	Discriminant	Galois group	Class group
22.0.178400853291024459894627.1	x^22 + 2x^20 + 5x^18 - x^17 + 6x^16 - 3x^15 + 9x^14 - x^13 + 7x^12 - 3x^11 + 13x^10 + 5x^8 + 3x^7 + 10x^6 + x^4 + 4x^2 + 2x + 1	\( -\,3^{11}\cdot 1003532779^{2} \)	22T47	Trivial (GRH)
22.0.1163485434252431102394067.1	x^22 - 2x^21 + 6x^20 - 12x^19 + 22x^18 - 40x^17 + 62x^16 - 97x^15 + 138x^14 - 177x^13 + 216x^12 - 233x^11 + 238x^10 - 226x^9 + 195x^8 - 164x^7 + 124x^6 - 85x^5 + 55x^4 - 29x^3 + 13x^2 - 5x + 1	\( -\,971^{2}\cdot 1867\cdot 25709231^{2} \)	22T53	Trivial (GRH)
22.0.2817611963463158891460983.1	x^22 - 4x^21 + 6x^20 - 8x^19 + 15x^18 - 9x^17 - 28x^16 + 46x^15 - 14x^14 + 23x^13 + 13x^12 - 297x^11 + 488x^10 - 240x^9 + 28x^8 - 134x^7 + 194x^6 - 130x^5 + 72x^4 - 28x^3 + 8x^2 - 2x + 1	\( -\,167^{11} \)	$D_{11}$ (as 22T2)	Trivial
22.0.3273714539904703691187619.1	x^22 - x^21 - 7x^19 + 8x^18 + 7x^17 + 17x^16 - 26x^15 - 35x^14 - 4x^13 + 68x^12 + 92x^11 + 10x^10 - 49x^9 - 27x^8 + 32x^7 + 57x^6 + 24x^5 - 13x^4 - 17x^3 - 3x^2 + 2x + 1	\( -\,61\cdot 1279\cdot 1609^{2}\cdot 4025911^{2} \)	22T53	Trivial (GRH)
22.0.4514211640352695524009371.1	x^22 + 2x^20 - 5x^19 - 4x^18 - 9x^17 + 8x^16 + 16x^15 + 29x^14 - 7x^13 - 29x^12 - 55x^11 + 4x^10 + 37x^9 + 57x^8 - 3x^7 - 30x^6 - 33x^5 + 7x^4 + 12x^3 + 5x^2 - 3x + 1	\( -\,11^{4}\cdot 181^{2}\cdot 101771\cdot 304099^{2} \)	22T53	Trivial (GRH)
22.0.6250054957079127310759347.1	x^22 - x^20 - 4x^19 + 3x^18 + 3x^17 + 6x^16 - 9x^15 + x^14 - 3x^13 + 9x^12 - 10x^11 + x^10 - 2x^9 + 8x^8 - 5x^7 - x^5 + 4x^4 - 2x^3 + x^2 + 1	\( -\,3^{11}\cdot 12917^{2}\cdot 459847^{2} \)	22T47	Trivial (GRH)
22.0.6293360649840402636051867.1	x^22 - x^21 - x^19 + 3x^18 - 3x^17 - x^16 + 5x^14 - 3x^13 - 2x^12 + x^11 + 6x^10 - 4x^9 - 2x^8 - x^7 + 5x^6 - 2x^5 - x^4 - 2x^3 + x^2 + x + 1	\( -\,3^{11}\cdot 64661^{2}\cdot 92179^{2} \)	22T47	Trivial (GRH)
22.0.64196743029301100734358828.1	x^22 - x^21 + 3x^20 - 7x^19 + 11x^18 - 18x^17 + 29x^16 - 40x^15 + 53x^14 - 67x^13 + 79x^12 - 87x^11 + 92x^10 - 90x^9 + 83x^8 - 73x^7 + 59x^6 - 43x^5 + 30x^4 - 18x^3 + 9x^2 - 4x + 1	\( -\,2^{2}\cdot 2029\cdot 7909899338257898069783 \)	22T59	Trivial (GRH)
22.0.75348325135501798832991875.1	x^22 - 4x^21 + 10x^20 - 22x^19 + 47x^18 - 79x^17 + 124x^16 - 169x^15 + 213x^14 - 229x^13 + 259x^12 - 192x^11 + 188x^10 - 90x^9 + 134x^8 - 14x^7 + 62x^6 - 19x^5 + 22x^4 - 12x^3 + 3x^2 - x + 1	\( -\,5^{4}\cdot 7^{6}\cdot 83^{5}\cdot 127^{4} \)	22T52	Trivial (GRH)
22.0.103946711888571010237690363.1	x^22 - 5x^21 + 15x^20 - 35x^19 + 68x^18 - 114x^17 + 170x^16 - 230x^15 + 285x^14 - 325x^13 + 343x^12 - 335x^11 + 306x^10 - 258x^9 + 202x^8 - 146x^7 + 97x^6 - 59x^5 + 32x^4 - 16x^3 + 7x^2 - 2x + 1	\( -\,79\cdot 22109\cdot 59513372976908430233 \)	22T59	Trivial (GRH)
22.0.110395262036162513388217347.1	x^22 - 4x^19 + 4x^16 - 4x^15 + x^14 - 6x^13 + 7x^12 - 3x^11 + 12x^10 + 2x^9 + 18x^8 + 4x^7 + 13x^6 + 5x^5 + 6x^4 + x^3 + 4x^2 - x + 1	\( -\,3^{11}\cdot 971^{2}\cdot 25709231^{2} \)	22T47	Trivial (GRH)
22.0.492568978448025181133471744.1	x^22 + 2x^20 - 5x^18 - 22x^16 + 29x^14 + 153x^12 + 72x^10 - 195x^8 - 158x^6 + 66x^4 + 77x^2 + 11	\( -\,2^{18}\cdot 11^{5}\cdot 19^{4}\cdot 547^{4} \)	22T52	Trivial (GRH)
22.0.577860666762298833296687104.1	x^22 - 2x^20 - 2x^19 + 5x^18 + 6x^17 - 5x^16 - 12x^15 + 2x^14 + 18x^13 + 4x^12 - 18x^11 - 11x^10 + 14x^9 + 14x^8 - 8x^7 - 11x^6 + 2x^5 + 8x^4 - 4x^2 + 1	\( -\,2^{30}\cdot 73^{2}\cdot 577\cdot 53149\cdot 3293113 \)	22T57	Trivial (GRH)
22.0.578978183833808423828407471.1	x^22 - 11x^21 + 67x^20 - 285x^19 + 929x^18 - 2433x^17 + 5271x^16 - 9630x^15 + 15091x^14 - 20633x^13 + 25057x^12 - 27453x^11 + 27302x^10 - 24426x^9 + 19254x^8 - 13050x^7 + 7570x^6 - 3890x^5 + 1921x^4 - 927x^3 + 362x^2 - 87x + 9	\( -\,271^{11} \)	$D_{11}$ (as 22T2)	Trivial (GRH)
22.0.1441291887151686135870128128.1	x^22 - 2x^20 - 2x^19 + 5x^18 + 6x^17 - 5x^16 - 12x^15 + 2x^14 + 18x^13 + 4x^12 - 18x^11 - 11x^10 + 14x^9 + 15x^8 - 8x^7 - 12x^6 + 2x^5 + 8x^4 - 4x^2 + 1	\( -\,2^{22}\cdot 10177\cdot 33765428299628041 \)	22T57	Trivial (GRH)
22.0.2613825179875044875466440704.1	x^22 + 6x^20 + 16x^18 + 18x^16 + 4x^14 + 6x^12 + 25x^10 + 3x^8 - 19x^6 - 4x^4 + 4x^2 + 1	\( -\,2^{22}\cdot 971^{2}\cdot 25709231^{2} \)	22T53	Trivial (GRH)
22.0.2988811416117414420033765003.1	x^22 - x^21 - 4x^20 + 3x^19 + 11x^18 - 6x^17 - 18x^16 + 2x^15 + 26x^14 - 8x^13 - 18x^12 + 23x^11 + 12x^10 - 27x^9 - 30x^8 + 23x^7 + 19x^6 + 3x^5 + 5x^4 - 26x^3 + 8x^2 + 2x + 1	\( -\,3^{11}\cdot 167^{10} \)	$D_{22}$ (as 22T3)	Trivial (GRH)
22.0.3101889720909924494411835627.1	x^22 - 2x^21 + 4x^20 - 2x^18 + 9x^17 - 4x^16 + 6x^15 + 4x^14 - 2x^13 + 10x^12 + 7x^10 + 4x^9 + 2x^8 + 11x^7 + x^6 + 3x^5 + 4x^4 + 2x^3 + 3x^2 - x + 1	\( -\,3^{11}\cdot 211441^{2}\cdot 625831^{2} \)	22T47	Trivial (GRH)
22.0.4395449323362095410329595467.1	x^22 - x^21 + 2x^20 + x^19 + 2x^18 - x^17 + 4x^15 - 6x^14 - 6x^13 - 3x^12 - x^11 - 2x^10 - 8x^9 + 8x^8 + 5x^7 + 7x^6 + 8x^5 + 8x^4 + 6x^3 + 4x^2 + 2x + 1	\( -\,3^{11}\cdot 19457^{2}\cdot 8095783^{2} \)	22T47	Trivial (GRH)
22.0.13109994191499930367061460371.1	x^22 + 44x^18 - 22x^17 + 55x^16 + 121x^15 + 187x^14 + 11x^13 + 594x^12 + 328x^11 + 836x^10 + 770x^9 + 814x^8 + 528x^7 + 374x^6 + 143x^5 + 11x^4 - 33x^3 - 11x^2 + 1	\( -\,11^{27} \)	$F_{11}$ (as 22T4)	Trivial (GRH)
22.0.15257581934366008831157764375.1	x^22 - 4x^21 + 18x^20 - 48x^19 + 125x^18 - 249x^17 + 478x^16 - 766x^15 + 1216x^14 - 1618x^13 + 2242x^12 - 2454x^11 + 2995x^10 - 2616x^9 + 2692x^8 - 1937x^7 + 1684x^6 - 1102x^5 + 757x^4 - 253x^3 + 163x^2 + 2x + 1	\( -\,5^{4}\cdot 7^{11}\cdot 83^{4}\cdot 127^{4} \)	22T46	Trivial (GRH)
22.0.39471584120695485887249589623.1	x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1	\( -\,23^{21} \)	$C_{22}$ (as 22T1)	$[3]$
22.0.45853693993707071407334096896.1	x^22 + 2x^20 + 3x^18 - 2x^16 - 7x^14 - 5x^12 + 4x^10 + 11x^8 - 2x^6 - 6x^4 + x^2 + 1	\( -\,2^{28}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4} \)	22T46	Trivial (GRH)
22.0.58158698878603618687895783643.1	x^22 - 3x^11 + 3	\( -\,3^{21}\cdot 11^{18} \)	$C_2\times F_{11}$ (as 22T6)	Trivial (GRH)
22.0.66009317547629600105613290523.1	x^22 - x^21 + 5x^20 + 2x^19 + 12x^18 + 13x^17 + 14x^16 + 63x^15 - 7x^14 + 68x^13 + 31x^12 + 19x^11 + 40x^10 - 71x^9 + 84x^8 - 79x^7 + 41x^6 - 38x^5 + 21x^4 - 11x^3 + 4x^2 - x + 1	\( -\,3^{11}\cdot 610429790897^{2} \)	22T47	Trivial (GRH)
22.0.70765994783241803539463274496.1	x^22 - 9x^20 + 37x^18 - 94x^16 + 166x^14 - 214x^12 + 207x^10 - 149x^8 + 81x^6 - 34x^4 + 12x^2 + 1	\( -\,2^{22}\cdot 167^{10} \)	$D_{22}$ (as 22T3)	Trivial (GRH)
22.0.70765994783241803539463274496.2	x^22 + 3x^20 + 4x^18 + 4x^16 + 11x^14 + 10x^12 + 4x^10 + 12x^8 + 7x^6 + 6x^4 + 4x^2 + 1	\( -\,2^{22}\cdot 167^{10} \)	22T32	Trivial (GRH)
22.0.70765994783241803539463274496.3	x^22 + x^20 - 7x^18 - 6x^16 + 23x^14 + x^12 - 24x^10 + 21x^8 - 17x^6 + 9x^4 - 2x^2 + 1	\( -\,2^{22}\cdot 167^{10} \)	22T32	Trivial (GRH)
22.0.73443346282868916473942769664.1	x^22 + 13x^20 + 75x^18 + 255x^16 + 572x^14 + 895x^12 + 999x^10 + 790x^8 + 425x^6 + 140x^4 + 21x^2 + 1	\( -\,2^{22}\cdot 211441^{2}\cdot 625831^{2} \)	22T53	Trivial (GRH)
22.0.115803236519047451106947869227.1	x^22 - 2x^21 + 5x^20 - 6x^19 + 10x^18 - 13x^17 + 3x^16 - 4x^15 - 15x^14 + 9x^13 - 23x^12 + 35x^11 + 5x^10 + 25x^9 + 40x^8 + 18x^7 + 38x^6 + 20x^4 - x^3 + 6x^2 - x + 1	\( -\,3^{11}\cdot 43^{2}\cdot 547^{2}\cdot 34374601^{2} \)	22T47	Trivial (GRH)
22.0.117045760309296676701139369984.1	x^22 + 2x^20 - x^16 - 7x^14 - 14x^12 - x^10 + 9x^8 + 15x^6 + 22x^4 + 10x^2 + 1	\( -\,2^{22}\cdot 2089^{2}\cdot 79966751^{2} \)	22T53	Trivial (GRH)
22.0.213248562554879935188951206691.1	x^22 - 4x^21 + 7x^20 - 12x^19 + 24x^18 - 33x^17 + 48x^16 - 51x^15 + 12x^14 - 2x^13 + 44x^12 + 193x^11 - 198x^10 - 426x^9 + 168x^8 + 372x^7 + 15x^6 - 99x^5 - 36x^4 - 36x^3 - 9x^2 + 18x + 9	\( -\,3^{20}\cdot 11^{19} \)	$F_{11}$ (as 22T4)	Trivial (GRH)
22.0.335585290345833574875265599163.1	x^22 - x + 1	\( -\,3697\cdot 90772326303985278570534379 \)	22T59	Trivial (GRH)
22.0.8744435969289427463345029296875.1	x^22 - 11x^21 + 55x^20 - 154x^19 + 220x^18 + 44x^17 - 913x^16 + 1991x^15 - 1958x^14 - 275x^13 + 3795x^12 - 5801x^11 + 4323x^10 - 517x^9 - 2475x^8 + 2772x^7 - 1188x^6 - 330x^5 + 803x^4 - 550x^3 + 209x^2 - 44x + 4	\( -\,5^{10}\cdot 11^{23} \)	$C_2\times F_{11}$ (as 22T6)	Trivial (GRH)
22.0.10046547996724887091059294601443.1	x^22 - x^21 + 7x^20 - 4x^19 + 31x^18 - 18x^17 + 77x^16 - 41x^15 + 140x^14 - 96x^13 + 153x^12 - 129x^11 + 145x^10 - 148x^9 + 84x^8 - 72x^7 + 94x^6 - 20x^5 + 39x^4 + 12x^3 + 18x^2 + 4x + 1	\( -\,3^{11}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2} \)	22T47	$[2]$ (GRH)
22.0.11817921128801381191090366840832.1	x^22 + 9x^20 + 37x^18 + 74x^16 + 22x^14 - 217x^12 - 442x^10 - 261x^8 + 291x^6 + 663x^4 + 501x^2 + 167	\( -\,2^{22}\cdot 167^{11} \)	22T29	Trivial (GRH)
22.0.11817921128801381191090366840832.2	x^22 - 6x^20 + 19x^18 - 15x^16 - 90x^14 + 259x^12 - 217x^10 + 142x^8 - 495x^6 + 761x^4 - 501x^2 + 167	\( -\,2^{22}\cdot 167^{11} \)	22T29	Trivial (GRH)
22.0.13329203788379546293009624459083.1	x^22 - x^21 + 8x^20 + x^19 + 33x^18 + 20x^17 + 97x^16 + 111x^15 + 195x^14 + 258x^13 + 328x^12 + 369x^11 + 392x^10 + 323x^9 + 362x^8 + 155x^7 + 199x^6 + 67x^5 + 63x^4 + 12x^3 + 11x^2 + 2x + 1	\( -\,3^{11}\cdot 8674315276967^{2} \)	22T47	Trivial (GRH)
22.0.13471519681654627790892423970816.1	x^22 + 12x^20 + 64x^18 + 200x^16 + 403x^14 + 544x^12 + 510x^10 + 358x^8 + 197x^6 + 73x^4 + 14x^2 + 1	\( -\,2^{22}\cdot 1792166448977^{2} \)	22T53	Trivial (GRH)
22.0.22378993818717495955548767565627.1	x^22 - 2x^21 + 3x^20 + 8x^19 - 22x^18 + 38x^17 - 4x^16 - 57x^15 + 146x^14 - 127x^13 + 42x^12 + 144x^11 - 154x^10 + 123x^9 - 19x^8 - 35x^7 + 41x^6 - 58x^5 + 35x^4 - 12x^3 + 7x^2 - 2x + 1	\( -\,3^{11}\cdot 1831^{8} \)	22T13	Trivial (GRH)
22.0.22378993818717495955548767565627.2	x^22 - 2x^21 + x^20 - 10x^19 + 18x^18 + 2x^17 + 31x^16 - 76x^15 - 19x^14 - 8x^13 + 188x^12 - 50x^11 - 76x^10 - 135x^9 + 130x^8 + 29x^7 + 42x^6 - 76x^5 + 11x^4 - 8x^3 + 13x^2 - 4x + 1	\( -\,3^{11}\cdot 1831^{8} \)	22T13	Trivial (GRH)
22.0.155979617226877172002898926703507.1	x^22 - 11x^21 + 76x^20 - 375x^19 + 1474x^18 - 4773x^17 + 13158x^16 - 31314x^15 + 65238x^14 - 119692x^13 + 194559x^12 - 280546x^11 + 359279x^10 - 407518x^9 + 408092x^8 - 358073x^7 + 272834x^6 - 177710x^5 + 97035x^4 - 42912x^3 + 14655x^2 - 3477x + 467	\( -\,23\cdot 2879\cdot 3371\cdot 56509^{2}\cdot 14792861^{2} \)	22T53	$[2]$ (GRH)
22.0.158889565336345086255331280912676.1	x^22 - 11x^21 + 66x^20 - 275x^19 + 880x^18 - 2277x^17 + 4917x^16 - 9042x^15 + 14355x^14 - 19855x^13 + 24068x^12 - 25650x^11 + 24035x^10 - 19723x^9 + 14058x^8 - 8646x^7 + 4653x^6 - 2343x^5 + 1210x^4 - 605x^3 + 231x^2 - 44x + 10	\( -\,2^{2}\cdot 3^{21}\cdot 11^{18}\cdot 683 \)	22T37	$[2]$ (GRH)
22.0.191943424957750480504146841291811.1	x^22 - 11x^21 + 66x^20 - 275x^19 + 847x^18 - 1980x^17 + 3454x^16 - 4070x^15 + 1100x^14 + 9482x^13 - 30690x^12 + 60224x^11 - 77803x^10 + 49665x^9 + 48642x^8 - 188375x^7 + 271315x^6 - 233860x^5 + 132748x^4 - 52624x^3 + 14960x^2 - 2816x + 256	\( -\,11^{31} \)	$D_{11}$ (as 22T2)	Trivial (GRH)
22.0.304011857053427966889939263171547.1	x^22 - x^21 + 11x^20 - 8x^19 + 73x^18 - 46x^17 + 301x^16 - 145x^15 + 883x^14 - 355x^13 + 1776x^12 - 498x^11 + 2527x^10 - 574x^9 + 2324x^8 - 251x^7 + 1358x^6 - 161x^5 + 400x^4 + 20x^3 + 51x^2 - 6x + 1	\( -\,3^{11}\cdot 23^{20} \)	$C_{22}$ (as 22T1)	$[23]$ (GRH)
22.0.328417397709776899721953240383603.1	x^22 - 2x^21 + 14x^20 - 22x^19 + 110x^18 - 154x^17 + 537x^16 - 588x^15 + 1719x^14 - 1556x^13 + 3922x^12 - 2650x^11 + 6120x^10 - 3124x^9 + 6945x^8 - 2284x^7 + 4957x^6 - 987x^5 + 2301x^4 - 102x^3 + 153x^2 + 9	\( -\,3^{15}\cdot 4784137656827^{2} \)	22T47	$[16]$ (GRH)
22.0.349622146420960826774166244950016.1	x^22 - 2x^11 + 2	\( -\,2^{32}\cdot 11^{22} \)	$C_2\times F_{11}$ (as 22T6)	Trivial (GRH)
22.0.420249828754162766851850612806803.1	x^22 - 3x^21 + 17x^20 - 32x^19 + 133x^18 - 221x^17 + 675x^16 - 925x^15 + 2270x^14 - 2774x^13 + 5421x^12 - 5457x^11 + 8435x^10 - 7261x^9 + 8780x^8 - 5447x^7 + 4182x^6 - 1619x^5 + 1047x^4 - 323x^3 + 152x^2 - 13x + 1	\( -\,3^{11}\cdot 421^{2}\cdot 115692385433^{2} \)	22T47	$[28]$ (GRH)
22.0.436946304674948987202161022509859.1	x^22 - 7x^21 + 27x^20 - 73x^19 + 238x^18 - 681x^17 + 1593x^16 - 3279x^15 + 6450x^14 - 11717x^13 + 18830x^12 - 25953x^11 + 31166x^10 - 32372x^9 + 28878x^8 - 22278x^7 + 14793x^6 - 8202x^5 + 3676x^4 - 1240x^3 + 279x^2 - 40x + 4	\( -\,3^{21}\cdot 11^{19}\cdot 683 \)	22T37	$[2]$ (GRH)
22.0.529866739430089519756710630129664.1	x^22 + 8x^20 + 29x^18 + 99x^16 + 222x^14 + 344x^12 + 382x^10 + 254x^8 + 145x^6 + 84x^4 + 32x^2 + 9	\( -\,2^{22}\cdot 1831^{8} \)	22T42	Trivial (GRH)