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 2408)

Label	Polynomial	Discriminant	Galois group	Class group
40.0.28789677222138897176527746894292024300433695316314697265625.1	x^40 - x^39 + x^35 - x^34 + x^30 - x^28 + x^25 - x^23 + x^20 - x^17 + x^15 - x^12 + x^10 - x^6 + x^5 - x + 1	\( 5^{30}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	$[10]$ (GRH)
40.0.29534212676193502024324377686070874915458261966705322265625.1	x^40 - x^35 + x^25 - x^20 + x^15 - x^5 + 1	\( 3^{20}\cdot 5^{70} \)	$C_2\times C_{20}$ (as 40T2)	$[11]$ (GRH)
40.0.9313225746154785156250000000000000000000000000000000000000000.1	x^40 - x^30 + x^20 - x^10 + 1	\( 2^{40}\cdot 5^{70} \)	$C_2\times C_{20}$ (as 40T2)	$[55]$ (GRH)
40.0.6856321115222930027351949403366821000578180886805057525634765625.1	x^40 - x^39 - 4x^38 + 7x^37 - x^36 - x^35 + 43x^34 - 99x^33 - 80x^32 + 377x^31 + 182x^30 - 676x^29 + 119x^28 - 544x^27 - 3261x^26 + 6247x^25 + 11925x^24 - 19250x^23 - 3176x^22 + 16639x^21 - 17018x^20 + 43346x^19 + 2424x^18 - 96822x^17 + 39515x^16 + 82301x^15 + 12498x^14 - 25677x^13 - 3560x^12 - 33345x^11 - 17836x^10 + 19768x^9 + 19004x^8 - 7029x^7 + 393x^6 + 406x^5 - 125x^4 + 46x^3 - 3x^2 - 3x + 1	\( 3^{20}\cdot 5^{30}\cdot 11^{32} \)	$C_2\times C_{20}$ (as 40T2)	$[55]$ (GRH)
40.0.675866784901662726441095609131171073613586486317217350006103515625.1	x^40 - 11x^35 + 89x^30 - 627x^25 + 4049x^20 - 20064x^15 + 91136x^10 - 360448x^5 + 1048576	\( 5^{70}\cdot 7^{20} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.2162050738724101412398710020310959104000000000000000000000000000000.1	x^40 - 9x^38 + 53x^36 - 260x^34 + 1156x^32 - 3971x^30 + 11685x^28 - 30590x^26 + 70035x^24 - 124361x^22 + 193618x^20 - 264514x^18 + 292022x^16 - 203056x^14 + 128969x^12 - 72116x^10 + 29056x^8 - 2353x^6 + 190x^4 - 15x^2 + 1	\( 2^{40}\cdot 5^{30}\cdot 11^{32} \)	$C_2\times C_{20}$ (as 40T2)	$[155]$ (GRH)
40.0.9765625000000000000000000000000000000000000000000000000000000000000.1	x^40 - 32x^30 + 1024x^20 - 32768x^10 + 1048576	\( 2^{60}\cdot 5^{70} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.9765625000000000000000000000000000000000000000000000000000000000000.2	x^40 + 32x^30 + 1024x^20 + 32768x^10 + 1048576	\( 2^{60}\cdot 5^{70} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.40.100383397447978918530459891214693626269465146363712847232818603515625.1	x^40 - x^39 - 39x^38 + 39x^37 + 702x^36 - 701x^35 - 7736x^34 + 7701x^33 + 58378x^32 - 57817x^31 - 319703x^30 + 314247x^29 + 1313873x^28 - 1277913x^27 - 4133168x^26 + 3963256x^25 + 10063407x^24 - 9469608x^23 - 19054236x^22 + 17493203x^21 + 28043254x^20 - 24933608x^19 - 31915288x^18 + 27222459x^17 + 27803858x^16 - 22476466x^15 - 18249278x^14 + 13764066x^13 + 8815690x^12 - 6077890x^11 - 3029168x^10 + 1857788x^9 + 703905x^8 - 369684x^7 - 102396x^6 + 43393x^5 + 8232x^4 - 2512x^3 - 288x^2 + 48x + 1	\( 3^{20}\cdot 5^{30}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	Trivial (GRH)
40.0.100383397447978918530459891214693626269465146363712847232818603515625.1	x^40 - x^39 + 11x^38 - 11x^37 + 77x^36 - 76x^35 + 439x^34 - 429x^33 + 2233x^32 - 2167x^31 + 9197x^30 - 8833x^29 + 32603x^28 - 30778x^27 + 102597x^26 - 95699x^25 + 285912x^24 - 263693x^23 + 659494x^22 - 595562x^21 + 1330759x^20 - 1163338x^19 + 2342802x^18 - 1938861x^17 + 3371093x^16 - 2519131x^15 + 3317622x^14 - 1836384x^13 + 2360500x^12 - 558855x^11 + 869342x^10 - 264572x^9 + 355025x^8 - 154704x^7 + 86679x^6 - 26432x^5 + 14707x^4 - 1397x^3 + 132x^2 - 12x + 1	\( 3^{20}\cdot 5^{30}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	$[2, 4210]$ (GRH)
40.0.100383397447978918530459891214693626269465146363712847232818603515625.2	x^40 - x^39 + 5x^38 - 5x^37 + 20x^36 - 19x^35 + 74x^34 - 65x^33 + 265x^32 - 210x^31 + 936x^30 - 1475x^29 + 4114x^28 - 6060x^27 + 15680x^26 - 21989x^25 + 56355x^24 - 75531x^23 + 197315x^22 - 252030x^21 + 682811x^20 - 826140x^19 + 1114445x^18 - 1435731x^17 + 1906140x^16 - 2365144x^15 + 3132335x^14 - 3532620x^13 + 4695244x^12 - 3931240x^11 + 5449401x^10 + 1139235x^9 + 238165x^8 + 49790x^7 + 10409x^6 + 2176x^5 + 455x^4 + 95x^3 + 20x^2 + 4x + 1	\( 3^{20}\cdot 5^{30}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.100383397447978918530459891214693626269465146363712847232818603515625.3	x^40 - x^39 + 21x^38 - 18x^37 + 249x^36 - 191x^35 + 2008x^34 - 1359x^33 + 12160x^32 - 7243x^31 + 57502x^30 - 29496x^29 + 218159x^28 - 94389x^27 + 671689x^26 - 234893x^25 + 1690845x^24 - 452550x^23 + 3479454x^22 - 637891x^21 + 5838877x^20 - 598784x^19 + 7925819x^18 - 188442x^17 + 8602640x^16 + 356201x^15 + 7327393x^14 + 688488x^13 + 4739830x^12 + 533615x^11 + 2212864x^10 + 232193x^9 + 670719x^8 + 9081x^7 + 109203x^6 - 5639x^5 + 12525x^4 - 994x^3 + 252x^2 + 12x + 1	\( 3^{20}\cdot 5^{30}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	$[2, 9262]$ (GRH)
40.0.2806502314667513790456400791754773417894971971642777758942872517738496.1	x^40 + 257x^32 + 14016x^24 + 105419x^16 + 23219x^8 + 1	\( 2^{120}\cdot 11^{32} \)	$C_2\times C_{20}$ (as 40T2)	$[2605]$ (GRH)
40.0.5698414109730419226674323998106663768936641645268537104129791259765625.1	x^40 - 31x^35 + 718x^30 - 14725x^25 + 282001x^20 - 3578175x^15 + 42397182x^10 - 444816117x^5 + 3486784401	\( 5^{70}\cdot 11^{20} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.31654584865659568778929513407372752241664000000000000000000000000000000.1	x^40 + 41x^38 + 778x^36 + 9065x^34 + 72556x^32 + 422839x^30 + 1855505x^28 + 6253910x^26 + 16367625x^24 + 33406879x^22 + 53106978x^20 + 65321146x^18 + 61394717x^16 + 43240794x^14 + 22168369x^12 + 7925719x^10 + 1852081x^8 + 255047x^6 + 17190x^4 + 360x^2 + 1	\( 2^{40}\cdot 5^{30}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	$[2, 85622]$ (GRH)
40.40.31654584865659568778929513407372752241664000000000000000000000000000000.1	x^40 - 39x^38 + 702x^36 - 7735x^34 + 58344x^32 - 319177x^30 + 1308973x^28 - 4102514x^26 + 9927425x^24 - 18613969x^22 + 26988270x^20 - 30037766x^18 + 25334997x^16 - 15882694x^14 + 7199257x^12 - 2269345x^10 + 470613x^8 - 59241x^6 + 4018x^4 - 120x^2 + 1	\( 2^{40}\cdot 5^{30}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	Trivial (GRH)
40.0.31654584865659568778929513407372752241664000000000000000000000000000000.2	x^40 + 11x^38 + 77x^36 + 440x^34 + 2244x^32 + 9273x^30 + 33033x^28 + 104786x^26 + 294635x^24 + 688611x^22 + 1416910x^20 + 2574154x^18 + 3942422x^16 + 4573316x^14 + 4694437x^12 + 4152720x^10 + 2752508x^8 + 863819x^6 + 263538x^4 + 73205x^2 + 14641	\( 2^{40}\cdot 5^{30}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.31654584865659568778929513407372752241664000000000000000000000000000000.3	x^40 + 5x^38 + 20x^36 + 75x^34 + 275x^32 + 1000x^30 + 3625x^28 + 13125x^26 + 47500x^24 + 171875x^22 + 621875x^20 + 859375x^18 + 1187500x^16 + 1640625x^14 + 2265625x^12 + 3125000x^10 + 4296875x^8 + 5859375x^6 + 7812500x^4 + 9765625x^2 + 9765625	\( 2^{40}\cdot 5^{30}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.32473210254684090614318847656250000000000000000000000000000000000000000.1	x^40 + 40x^38 + 740x^36 + 8400x^34 + 65450x^32 + 371009x^30 + 1582270x^28 + 5178645x^26 + 13151125x^24 + 26030250x^22 + 40123776x^20 + 47888645x^18 + 43779420x^16 + 30152050x^14 + 15277900x^12 + 5507149x^10 + 1345115x^8 + 206465x^6 + 17450x^4 + 600x^2 + 1	\( 2^{40}\cdot 3^{20}\cdot 5^{70} \)	$C_2\times C_{20}$ (as 40T2)	$[237710]$ (GRH)
40.40.32473210254684090614318847656250000000000000000000000000000000000000000.1	x^40 - 40x^38 + 740x^36 - 8400x^34 + 65450x^32 - 371007x^30 + 1582210x^28 - 5177835x^26 + 13144625x^24 - 25995750x^22 + 39996264x^20 - 47552155x^18 + 43139880x^16 - 29279950x^14 + 14438100x^12 - 4952883x^10 + 1106455x^8 - 144655x^6 + 9150x^4 - 200x^2 + 1	\( 2^{40}\cdot 3^{20}\cdot 5^{70} \)	$C_2\times C_{20}$ (as 40T2)	Trivial (GRH)
40.0.32473210254684090614318847656250000000000000000000000000000000000000000.2	x^40 + 20x^38 + 230x^36 + 1800x^34 + 10625x^32 + 49005x^30 + 181750x^28 + 546975x^26 + 1346750x^24 + 2703375x^22 + 4412520x^20 + 5771300x^18 + 5985150x^16 + 4782125x^14 + 2915250x^12 + 1285650x^10 + 409750x^8 + 82625x^6 + 11250x^4 + 625x^2 + 25	\( 2^{40}\cdot 3^{20}\cdot 5^{70} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.32473210254684090614318847656250000000000000000000000000000000000000000.3	x^40 + 243x^30 + 59049x^20 + 14348907x^10 + 3486784401	\( 2^{40}\cdot 3^{20}\cdot 5^{70} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.40126953504928778716867347648517224229883090465646395672541598175985664.1	x^40 - 4x^38 + 14x^36 - 48x^34 + 164x^32 - 560x^30 + 1912x^28 - 6528x^26 + 22288x^24 - 76096x^22 + 259808x^20 - 152192x^18 + 89152x^16 - 52224x^14 + 30592x^12 - 17920x^10 + 10496x^8 - 6144x^6 + 3584x^4 - 2048x^2 + 1024	\( 2^{110}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	$[5731]$ (GRH)
40.0.40126953504928778716867347648517224229883090465646395672541598175985664.2	x^40 + 4x^38 + 14x^36 + 48x^34 + 164x^32 + 560x^30 + 1912x^28 + 6528x^26 + 22288x^24 + 76096x^22 + 259808x^20 + 152192x^18 + 89152x^16 + 52224x^14 + 30592x^12 + 17920x^10 + 10496x^8 + 6144x^6 + 3584x^4 + 2048x^2 + 1024	\( 2^{110}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.67330470569637410331240297486633042732017118041235378120152501254022721.1	x^40 - x^39 + 20x^38 - 17x^37 + 226x^36 - 172x^35 + 1735x^34 - 1174x^33 + 9997x^32 - 6058x^31 + 44934x^30 - 24189x^29 + 161911x^28 - 77302x^27 + 472811x^26 - 197858x^25 + 1127150x^24 - 410723x^23 + 2190299x^22 - 682496x^21 + 3457565x^20 - 911552x^19 + 4383590x^18 - 948272x^17 + 4405640x^16 - 773063x^15 + 3426005x^14 - 457001x^13 + 2008708x^12 - 207142x^11 + 846197x^10 - 53834x^9 + 244002x^8 - 13431x^7 + 43098x^6 - 33x^5 + 4180x^4 - 220x^3 + 155x^2 + 10x + 1	\( 3^{20}\cdot 41^{38} \)	$C_2\times C_{20}$ (as 40T2)	$[8, 8, 8, 136]$ (GRH)
40.0.80991088329663621512136783946706428882352994235065987550082919086927689.1	x^40 - x^39 - x^38 + 7x^37 - 12x^36 - 3x^35 + 58x^34 - 121x^33 + 29x^32 + 454x^31 - 1170x^30 - 413x^29 + 4482x^28 - 9698x^27 + 2592x^26 + 35971x^25 - 93393x^24 + 60913x^23 + 261981x^22 - 865292x^21 + 865161x^20 + 1730608x^19 + 1651223x^18 + 944081x^17 + 80422x^16 - 555516x^15 - 782673x^14 - 616850x^13 - 281134x^12 + 50690x^11 + 392197x^10 + 232437x^9 + 29331x^8 - 123822x^7 - 181683x^6 - 150660x^5 - 69255x^4 + 15309x^3 + 65610x^2 + 78732x + 59049	\( 11^{36}\cdot 13^{30} \)	$C_2\times C_{20}$ (as 40T2)	$[1525]$ (GRH)
40.0.156901413259422267514584360713728302021067834330649115145206451416015625.1	x^40 - x^39 - 13x^38 + 20x^37 + 84x^36 - 41x^35 - 359x^34 - 768x^33 + 987x^32 + 9239x^31 - 11046x^30 - 44916x^29 + 133166x^28 - 66478x^27 - 944653x^26 + 1164448x^25 + 4678770x^24 - 4718023x^23 - 13472506x^22 - 1446413x^21 + 34263783x^20 + 108753318x^19 - 122648476x^18 - 339047952x^17 + 362849376x^16 + 551628320x^15 - 458037312x^14 - 301074432x^13 + 809304320x^12 - 994491904x^11 - 1301196800x^10 + 916971520x^9 + 1464213504x^8 - 551878656x^7 - 96944128x^6 + 86966272x^5 - 1048576x^4 + 17432576x^3 - 4718592x^2 - 1572864x + 1048576	\( 5^{30}\cdot 7^{20}\cdot 11^{32} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.160978304786984968542969308088509683418720896952436305582523345947265625.1	x^40 - 61x^35 + 3964x^30 - 256627x^25 + 16617499x^20 + 62360361x^15 + 234070236x^10 + 875283327x^5 + 3486784401	\( 5^{70}\cdot 13^{20} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.2267074515408363362607389758257584253435904000000000000000000000000000000.1	x^40 - 18x^38 + 212x^36 - 2080x^34 + 18496x^32 - 127072x^30 + 747840x^28 - 3915520x^26 + 17928960x^24 - 63672832x^22 + 198264832x^20 - 541724672x^18 + 1196122112x^16 - 1663434752x^14 + 2113028096x^12 - 2363097088x^10 + 1904214016x^8 - 308412416x^6 + 49807360x^4 - 7864320x^2 + 1048576	\( 2^{60}\cdot 5^{30}\cdot 11^{32} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.2267074515408363362607389758257584253435904000000000000000000000000000000.2	x^40 + 18x^38 + 212x^36 + 2080x^34 + 18496x^32 + 127072x^30 + 747840x^28 + 3915520x^26 + 17928960x^24 + 63672832x^22 + 198264832x^20 + 541724672x^18 + 1196122112x^16 + 1663434752x^14 + 2113028096x^12 + 2363097088x^10 + 1904214016x^8 + 308412416x^6 + 49807360x^4 + 7864320x^2 + 1048576	\( 2^{60}\cdot 5^{30}\cdot 11^{32} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.10240000000000000000000000000000000000000000000000000000000000000000000000.1	x^40 + 40x^38 + 740x^36 + 8400x^34 + 65450x^32 + 371008x^30 + 1582240x^28 + 5178240x^26 + 13147875x^24 + 26013000x^22 + 40060019x^20 + 47720380x^18 + 43459480x^16 + 29715200x^14 + 14855725x^12 + 5226012x^10 + 1221495x^8 + 172920x^6 + 12475x^4 + 300x^2 + 1	\( 2^{80}\cdot 5^{70} \)	$C_2\times C_{20}$ (as 40T2)	$[542102]$ (GRH)
40.40.10240000000000000000000000000000000000000000000000000000000000000000000000.1	x^40 - 40x^38 + 740x^36 - 8400x^34 + 65450x^32 - 371008x^30 + 1582240x^28 - 5178240x^26 + 13147875x^24 - 26013000x^22 + 40060019x^20 - 47720380x^18 + 43459480x^16 - 29715200x^14 + 14855725x^12 - 5226012x^10 + 1221495x^8 - 172920x^6 + 12475x^4 - 300x^2 + 1	\( 2^{80}\cdot 5^{70} \)	$C_2\times C_{20}$ (as 40T2)	Trivial (GRH)
40.0.10240000000000000000000000000000000000000000000000000000000000000000000000.2	x^40 + 60x^36 + 1450x^32 + 18100x^28 + 124375x^24 + 462515x^20 + 846200x^16 + 609125x^12 + 139875x^8 + 6875x^4 + 25	\( 2^{80}\cdot 5^{70} \)	$C_2\times C_{20}$ (as 40T2)	$[66110]$ (GRH)
40.0.21231778848647571139402736714989215192335577851351941759145128045204996096.1	x^40 + 39x^38 + 703x^36 + 7770x^34 + 58905x^32 + 324632x^30 + 1344904x^28 + 4272048x^26 + 10518300x^24 + 20160075x^22 + 30045015x^20 + 34597290x^18 + 30421755x^16 + 20058300x^14 + 9657700x^12 + 3268760x^10 + 735471x^8 + 100947x^6 + 7315x^4 + 210x^2 + 1	\( 2^{40}\cdot 41^{38} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.34425379066961841688086546115648602095493657770930440165102481842041015625.1	x^40 - 101x^35 + 11225x^30 - 1237149x^25 + 136446449x^20 + 1266840576x^15 + 11770265600x^10 + 108447924224x^5 + 1099511627776	\( 5^{70}\cdot 17^{20} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.40.41090000389047069406072163992081637611400284636821909168682596532209319936.1	x^40 - 40x^38 + 740x^36 - 8400x^34 + 65449x^32 - 370976x^30 + 1581776x^28 - 5174208x^26 + 13124476x^24 - 25917344x^22 + 39776912x^20 - 47106624x^18 + 42484835x^16 - 28593712x^14 + 13942072x^12 - 4719648x^10 + 1042879x^8 - 137208x^6 + 9260x^4 - 240x^2 + 1	\( 2^{120}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	Trivial (GRH)
40.0.41090000389047069406072163992081637611400284636821909168682596532209319936.1	x^40 + 40x^38 + 740x^36 + 8400x^34 + 65449x^32 + 370976x^30 + 1581776x^28 + 5174208x^26 + 13124476x^24 + 25917344x^22 + 39776912x^20 + 47106624x^18 + 42484835x^16 + 28593712x^14 + 13942072x^12 + 4719648x^10 + 1042879x^8 + 137208x^6 + 9260x^4 + 240x^2 + 1	\( 2^{120}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	$[1068050]$ (GRH)
40.0.41090000389047069406072163992081637611400284636821909168682596532209319936.2	x^40 + 385x^32 + 38720x^24 + 842523x^16 + 1449459x^8 + 14641	\( 2^{120}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.253281988439137179457025436268249370758366908512630642001927803052192601489.1	x^40 - x^39 + 7x^38 - 12x^37 + 52x^36 - 116x^35 + 409x^34 - 1041x^33 + 3327x^32 - 9048x^31 + 27560x^30 + 44511x^29 + 108474x^28 + 195200x^27 + 472595x^26 + 762568x^25 + 2159728x^24 + 2693075x^23 + 10555266x^22 + 7000344x^21 + 56864599x^20 - 7000344x^19 + 10555266x^18 - 2693075x^17 + 2159728x^16 - 762568x^15 + 472595x^14 - 195200x^13 + 108474x^12 - 44511x^11 + 27560x^10 + 9048x^9 + 3327x^8 + 1041x^7 + 409x^6 + 116x^5 + 52x^4 + 12x^3 + 7x^2 + x + 1	\( 11^{36}\cdot 17^{30} \)	$C_2\times C_{20}$ (as 40T2)	$[167977]$ (GRH)
40.0.318399460049560753522799707977372109246605447196998284198343753814697265625.1	x^40 - 101x^35 + 7076x^30 - 399051x^25 + 18191651x^20 - 1247034375x^15 + 69101562500x^10 - 3082275390625x^5 + 95367431640625	\( 5^{70}\cdot 19^{20} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.455114956604101938631100439919192819024746180307118297554552555084228515625.1	x^40 - x^39 - x^38 + 19x^37 - 24x^36 + 53x^35 + 236x^34 - 529x^33 + 884x^32 + 3395x^31 - 2402x^30 + 4304x^29 + 47648x^28 - 36412x^27 - 24459x^26 + 155327x^25 - 180921x^24 - 713657x^23 + 926706x^22 - 293393x^21 - 1658812x^20 + 3360939x^19 + 3678122x^18 - 6001107x^17 + 7599798x^16 + 4424280x^15 - 12065200x^14 - 5513654x^13 + 11699025x^12 - 5547842x^11 - 5967172x^10 + 6548168x^9 + 2801471x^8 - 3833465x^7 - 78700x^6 + 576250x^5 + 228750x^4 + 1281250x^3 - 734375x^2 - 312500x + 390625	\( 5^{30}\cdot 31^{36} \)	$C_2\times C_{20}$ (as 40T2)	$[2, 4, 4, 20, 60]$ (GRH)
40.40.1841563260274838293179920707241561880108912129957310865805656528472900390625.1	x^40 - x^39 - 58x^38 + 53x^37 + 1486x^36 - 1226x^35 - 22237x^34 + 16342x^33 + 216813x^32 - 139848x^31 - 1457140x^30 + 812165x^29 + 6977251x^28 - 3307776x^27 - 24306985x^26 + 9650330x^25 + 62453182x^24 - 20449687x^23 - 119327033x^22 + 31725068x^21 + 170133237x^20 - 36107412x^19 - 180748378x^18 + 30022768x^17 + 142090232x^16 - 18029877x^15 - 81534233x^14 + 7661653x^13 + 33400952x^12 - 2229292x^11 - 9440783x^10 + 421058x^9 + 1747746x^8 - 46431x^7 - 195228x^6 + 2013x^5 + 11440x^4 + 110x^3 - 265x^2 - 10x + 1	\( 5^{20}\cdot 41^{38} \)	$C_2\times C_{20}$ (as 40T2)	Trivial (GRH)
40.0.2297193591531201418681029625209696069890454162435033694840967655181884765625.1	x^40 - x^39 + 22x^38 - 22x^37 + 308x^36 - 307x^35 + 3519x^34 - 3498x^33 + 35882x^32 - 35596x^31 + 296429x^30 - 293150x^29 + 2110547x^28 - 2075282x^27 + 13374064x^26 - 13145659x^25 + 75162890x^24 - 74206309x^23 + 351383846x^22 - 349430224x^21 + 1448005637x^20 - 1445089910x^19 + 5267002532x^18 - 5024257635x^17 + 15902796162x^16 - 13906613709x^15 + 35229430126x^14 - 25437652416x^13 + 65099228501x^12 - 34784643894x^11 + 95934413763x^10 - 61702659106x^9 + 117125088960x^8 - 82784517200x^7 + 52680368047x^6 - 26420704463x^5 + 15228656432x^4 - 3213685552x^3 + 662073632x^2 - 126019697x + 20151121	\( 5^{30}\cdot 7^{20}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.40.2297193591531201418681029625209696069890454162435033694840967655181884765625.1	x^40 - x^39 - 78x^38 + 78x^37 + 2808x^36 - 2797x^35 - 61891x^34 + 61132x^33 + 934252x^32 - 910316x^31 - 10236731x^30 + 9779770x^29 + 84201027x^28 - 78304622x^27 - 530401956x^26 + 476024791x^25 + 2587528870x^24 - 2217966289x^23 - 9822625214x^22 + 7941388686x^21 + 28998395977x^20 - 21780235070x^19 - 66197093248x^18 + 45356621385x^17 + 115530235482x^16 - 70671998879x^15 - 151353912514x^14 + 80642756914x^13 + 144757030391x^12 - 65437791794x^11 - 96911211847x^10 + 36333104654x^9 + 42561792020x^8 - 13143856660x^7 - 11039037933x^6 + 2893122177x^5 + 1401644442x^4 - 331925242x^3 - 55346148x^2 + 11969793x - 440429	\( 5^{30}\cdot 7^{20}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.2297193591531201418681029625209696069890454162435033694840967655181884765625.2	x^40 - x^39 + 10x^38 - 10x^37 + 80x^36 - 69x^35 + 589x^34 - 380x^33 + 4180x^32 - 1540x^31 + 29261x^30 - 73920x^29 + 277429x^28 - 662420x^27 + 2172130x^26 - 4823929x^25 + 15359600x^24 - 31939171x^23 + 102866780x^22 - 199019700x^21 + 668412581x^20 - 1182457980x^19 + 2618352220x^18 - 5055544111x^17 + 10626053880x^16 - 19553743119x^15 + 40886456620x^14 - 65624674550x^13 + 140732503379x^12 - 148285290440x^11 + 374504727081x^10 + 279391609420x^9 + 208525783180x^8 + 155444907860x^7 + 116259627649x^6 + 86168888091x^5 + 65388316510x^4 + 46574338690x^3 + 38584598580x^2 + 21221529219x + 25937424601	\( 5^{30}\cdot 7^{20}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.2297193591531201418681029625209696069890454162435033694840967655181884765625.3	x^40 - 18x^39 + 152x^38 - 800x^37 + 3064x^36 - 10008x^35 + 32049x^34 - 101440x^33 + 296109x^32 - 789250x^31 + 2021570x^30 - 5108510x^29 + 12425384x^28 - 28608228x^27 + 63471622x^26 - 137818978x^25 + 290635519x^24 - 589420568x^23 + 1156452894x^22 - 2209847288x^21 + 4106579731x^20 - 7379250472x^19 + 12845371352x^18 - 21684279952x^17 + 35554968308x^16 - 56311944536x^15 + 86289035972x^14 - 127319828864x^13 + 181966505414x^12 - 248991356996x^11 + 328793281400x^10 - 410912987056x^9 + 496328054189x^8 - 557798882542x^7 + 606994857502x^6 - 589952434929x^5 + 562299424896x^4 - 442214109777x^3 + 359771906472x^2 - 185412094428x + 113102086801	\( 5^{30}\cdot 7^{20}\cdot 11^{36} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.40.2356601762749139913517942415268160462338276062155273393727838993072509765625.1	x^40 - 80x^38 + 2960x^36 - 11x^35 - 67200x^34 + 770x^33 + 1047200x^32 - 24640x^31 - 11872224x^30 + 477400x^29 + 101261440x^28 - 6252400x^27 - 662762880x^26 + 58522739x^25 + 3365024000x^24 - 403616950x^23 - 13309824000x^22 + 2084212900x^21 + 40956171311x^20 - 8107946000x^19 - 97386692440x^18 + 23720246000x^17 + 176698891480x^16 - 51717568485x^15 - 239841990400x^14 + 82634574550x^13 + 236443720400x^12 - 94254254600x^11 - 161908455840x^10 + 73797867000x^9 + 71681548800x^8 - 37349092000x^7 - 17934217600x^6 + 11028952605x^5 + 1748896000x^4 - 1531206050x^3 + 60864000x^2 + 46652100x - 3248255	\( 3^{20}\cdot 5^{70}\cdot 7^{20} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.2356601762749139913517942415268160462338276062155273393727838993072509765625.1	x^40 - 151x^35 + 25926x^30 - 4386701x^25 + 743410601x^20 + 13708440625x^15 + 253183593750x^10 + 4608154296875x^5 + 95367431640625	\( 3^{20}\cdot 5^{70}\cdot 7^{20} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.2356601762749139913517942415268160462338276062155273393727838993072509765625.2	x^40 + 40x^38 + 920x^36 - 11x^35 + 14400x^34 - 550x^33 + 170000x^32 - 12760x^31 + 1568160x^30 - 195800x^29 + 11635630x^28 - 2147200x^27 + 70128960x^26 - 17908429x^25 + 346655600x^24 - 115196290x^23 + 1404165600x^22 - 582311180x^21 + 4665057839x^20 - 2298348800x^19 + 12597743150x^18 - 7107601600x^17 + 27443275180x^16 - 16844703909x^15 + 47090141000x^14 - 30216401600x^13 + 62111345600x^12 - 38642127260x^11 + 58711819680x^10 - 33262310400x^9 + 36511599630x^8 - 14898545200x^7 + 9859544360x^6 - 1520467971x^5 + 964792600x^4 - 59831420x^3 + 79872000x^2 + 3440580x + 160801	\( 3^{20}\cdot 5^{70}\cdot 7^{20} \)	$C_2\times C_{20}$ (as 40T2)	n/a
40.0.2356601762749139913517942415268160462338276062155273393727838993072509765625.3	x^40 + 60x^38 + 1770x^36 - 11x^35 + 33600x^34 - 595x^33 + 455875x^32 - 15470x^31 + 4661804x^30 - 253575x^29 + 37017890x^28 - 2905350x^27 + 232121040x^26 - 24470367x^25 + 1159115225x^24 - 155450395x^23 + 4619721900x^22 - 753390260x^21 + 14652746289x^20 - 2789292800x^19 + 36699315280x^18 - 7836540800x^17 + 71660476320x^16 - 16477469024x^15 + 107073932800x^14 - 25427153280x^13 + 119352953600x^12 - 28074777600x^11 + 95896866816x^10 - 21629696000x^9 + 53124833280x^8 - 11098112000x^7 + 18835046400x^6 - 3369566208x^5 + 3815833600x^4 - 429260800x^3 + 288358400x^2 + 10485760x + 1048576	\( 3^{20}\cdot 5^{70}\cdot 7^{20} \)	$C_2\times C_{20}$ (as 40T2)	n/a