Number field search results

Results (1-50 of 3589 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
40.0.597...625.1	x^40 - 10x^35 + 139x^30 + 5380x^25 + 28941x^20 - 5380x^15 + 139x^10 + 10x^5 + 1	$40$	[0,20]	$5^{50}\cdot 11^{20}$	$2$	$24.797554190130167$				$C_{20}\times D_5$ (as 40T149)	$[2]$	$10$	$19$	$1598432511220.758$
40.0.287...625.1	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	$40$	[0,20]	$5^{30}\cdot 11^{36}$	$2$	$28.9388267568$	✓	✓	✓	$C_2\times C_{20}$ (as 40T2)	$[10]$	$110$	$19$	$30395381425048.965$
40.0.295...625.1	x^40 - x^35 + x^25 - x^20 + x^15 - x^5 + 1	$40$	[0,20]	$3^{20}\cdot 5^{70}$	$2$	$28.9573046322$	✓	✓	✓	$C_2\times C_{20}$ (as 40T2)	$[11]$	$150$	$19$	$32146857615014.19$
40.0.118...536.1	x^40 + x^38 - x^34 - x^32 + x^28 + x^26 - x^22 - x^20 - x^18 + x^14 + x^12 - x^8 - x^6 + x^2 + 1	$40$	[0,20]	$2^{40}\cdot 3^{20}\cdot 11^{36}$	$3$	$29.9808567728$	✓	✓	✓	$C_2^2\times C_{10}$ (as 40T7)	$[11]$	$132$	$19$	$45016485591237.79$
40.0.931...000.1	x^40 - x^30 + x^20 - x^10 + 1	$40$	[0,20]	$2^{40}\cdot 5^{70}$	$2$	$33.4370152488$	✓	✓	✓	$C_2\times C_{20}$ (as 40T2)	$[55]$	$100$	$19$	$144312257071955.8$
40.0.102...625.1	x^40 - x^39 - x^38 + 4x^37 - 4x^36 - 4x^35 + 17x^34 - 17x^33 - 17x^32 + 72x^31 - 72x^30 + 127x^29 + 106x^28 - 504x^27 + 491x^26 + 496x^25 - 2088x^24 + 2091x^23 + 2090x^22 - 8856x^21 + 8855x^20 + 8856x^19 + 2090x^18 - 2091x^17 - 2088x^16 - 496x^15 + 491x^14 + 504x^13 + 106x^12 - 127x^11 - 72x^10 - 72x^9 - 17x^8 + 17x^7 + 17x^6 + 4x^5 - 4x^4 - 4x^3 - x^2 + x + 1	$40$	[0,20]	$3^{20}\cdot 5^{20}\cdot 11^{36}$	$3$	$33.5196168839$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	$[22]$	$66$	$19$	$138297149643015.1$
40.0.373...536.1	x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1	$40$	[0,20]	$2^{80}\cdot 11^{36}$	$2$	$34.6189114567$	✓	✓	✓	$C_2^2\times C_{10}$ (as 40T7)	$[55]$	$88$	$19$	$172972974175441.34$
40.0.791...161.1	x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + 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	$40$	[0,20]	$41^{39}$	$1$	$37.3649375129$	✓	✓	✓	$C_{40}$ (as 40T1)	$[11, 11]$	$82$	$19$	$310417721980536.1$
40.0.324...000.1	x^40 - 3x^38 + 8x^36 - 21x^34 + 55x^32 - 144x^30 + 377x^28 - 987x^26 + 2584x^24 - 6765x^22 + 17711x^20 - 6765x^18 + 2584x^16 - 987x^14 + 377x^12 - 144x^10 + 55x^8 - 21x^6 + 8x^4 - 3x^2 + 1	$40$	[0,20]	$2^{40}\cdot 5^{20}\cdot 11^{36}$	$3$	$38.7051196621$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	$[62]$	$44$	$19$	$645826241875575.0$
40.0.685...625.1	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	$40$	[0,20]	$3^{20}\cdot 5^{30}\cdot 11^{32}$	$3$	$39.4368554623$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	$[55]$	$30$	$19$	$636238292225226.0$
40.0.860...761.1	x^40 - x^39 + 2x^38 - 5x^37 + 5x^36 - 10x^35 + 17x^34 - 17x^33 + 34x^32 - 45x^31 + 45x^30 - 23x^29 + 22x^28 + 45x^27 - 157x^26 + 250x^25 - 585x^24 + 969x^23 - 1426x^22 + 2565x^21 - 3589x^20 + 5130x^19 - 5704x^18 + 7752x^17 - 9360x^16 + 8000x^15 - 10048x^14 + 5760x^13 + 5632x^12 - 11776x^11 + 46080x^10 - 92160x^9 + 139264x^8 - 139264x^7 + 278528x^6 - 327680x^5 + 327680x^4 - 655360x^3 + 524288x^2 - 524288x + 1048576	$40$	[0,20]	$3^{20}\cdot 7^{20}\cdot 11^{36}$	$3$	$39.6609455568$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	not computed	$66$	$19$	$$
40.0.119...041.1	x^40 - x + 1	$40$	[0,20]	$89\cdot 2963\cdot 2969\cdot 36703533640127\cdot 206798756592464370511\cdot 2015339302026829599091$	$6$	$39.9906437988$			✓	$S_{40}$ (as 40T315842)	trivial	$2$	$19$	$9483736502678452.0$
40.2.122...959.1	x^40 - x - 1	$40$	[2,19]	$-\,25788481\cdot 47\!\cdots\!39$	$2$	$40.0092716221$			✓	$S_{40}$ (as 40T315842)	trivial	$2$	$20$	$8469994147830637.0$
40.0.124...736.1	x^40 - 2x^38 + 8x^34 - 16x^32 + 64x^28 - 128x^26 + 512x^22 - 1024x^20 + 2048x^18 - 8192x^14 + 16384x^12 - 65536x^8 + 131072x^6 - 524288x^2 + 1048576	$40$	[0,20]	$2^{60}\cdot 3^{20}\cdot 11^{36}$	$3$	$42.3993342597$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	not computed	$66$	$19$	$$
40.0.124...736.2	x^40 + 2x^38 - 8x^34 - 16x^32 + 64x^28 + 128x^26 - 512x^22 - 1024x^20 - 2048x^18 + 8192x^14 + 16384x^12 - 65536x^8 - 131072x^6 + 524288x^2 + 1048576	$40$	[0,20]	$2^{60}\cdot 3^{20}\cdot 11^{36}$	$3$	$42.3993342597$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	not computed	$66$	$19$	$$
40.0.675...625.1	x^40 - 11x^35 + 89x^30 - 627x^25 + 4049x^20 - 20064x^15 + 91136x^10 - 360448x^5 + 1048576	$40$	[0,20]	$5^{70}\cdot 7^{20}$	$2$	$44.2330134663$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	not computed	$50$	$19$	$$
40.0.216...000.1	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	$40$	[0,20]	$2^{40}\cdot 5^{30}\cdot 11^{32}$	$3$	$45.5377582343$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	$[155]$	$20$	$19$	$2347083738648341.5$
40.0.271...136.1	x^40 + 3x^38 + 5x^36 + 3x^34 - 11x^32 - 45x^30 - 91x^28 - 93x^26 + 85x^24 + 627x^22 + 1541x^20 + 2508x^18 + 1360x^16 - 5952x^14 - 23296x^12 - 46080x^10 - 45056x^8 + 49152x^6 + 327680x^4 + 786432x^2 + 1048576	$40$	[0,20]	$2^{40}\cdot 7^{20}\cdot 11^{36}$	$3$	$45.796515187$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	not computed	$44$	$19$	$$
40.0.890...496.1	x^40 - 25x^36 + 441x^32 - 3794x^28 + 23626x^24 - 66403x^20 + 133864x^16 - 62097x^12 + 23622x^8 - 155x^4 + 1	$40$	[0,20]	$2^{80}\cdot 3^{20}\cdot 11^{32}$	$3$	$47.1774830006$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	$[5, 5, 5]$	$24$	$19$	$7121371366090164.0$
40.0.976...000.1	x^40 - 32x^30 + 1024x^20 - 32768x^10 + 1048576	$40$	[0,20]	$2^{60}\cdot 5^{70}$	$2$	$47.2870804502$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	not computed	$50$	$19$	$$
40.0.976...000.2	x^40 + 32x^30 + 1024x^20 + 32768x^10 + 1048576	$40$	[0,20]	$2^{60}\cdot 5^{70}$	$2$	$47.2870804502$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	not computed	$50$	$19$	$$
40.40.100...625.1	x^40 - x^39 - 39x^38 + 39x^37 + 702x^36 - 701x^35 - 7736x^34 + 7701x^33 + 58378x^32 - 57817x^31 - 319703x^30 + 314247x^29 + 1313873x^28 - 1277913x^27 - 4133168x^26 + 3963256x^25 + 10063407x^24 - 9469608x^23 - 19054236x^22 + 17493203x^21 + 28043254x^20 - 24933608x^19 - 31915288x^18 + 27222459x^17 + 27803858x^16 - 22476466x^15 - 18249278x^14 + 13764066x^13 + 8815690x^12 - 6077890x^11 - 3029168x^10 + 1857788x^9 + 703905x^8 - 369684x^7 - 102396x^6 + 43393x^5 + 8232x^4 - 2512x^3 - 288x^2 + 48x + 1	$40$	[40,0]	$3^{20}\cdot 5^{30}\cdot 11^{36}$	$3$	$50.1235182543$		✓	✓	$C_2\times C_{20}$ (as 40T2)	trivial	$2$	$39$	$1967499665744724500000$
40.0.100...625.1	x^40 - x^39 + 11x^38 - 11x^37 + 77x^36 - 76x^35 + 439x^34 - 429x^33 + 2233x^32 - 2167x^31 + 9197x^30 - 8833x^29 + 32603x^28 - 30778x^27 + 102597x^26 - 95699x^25 + 285912x^24 - 263693x^23 + 659494x^22 - 595562x^21 + 1330759x^20 - 1163338x^19 + 2342802x^18 - 1938861x^17 + 3371093x^16 - 2519131x^15 + 3317622x^14 - 1836384x^13 + 2360500x^12 - 558855x^11 + 869342x^10 - 264572x^9 + 355025x^8 - 154704x^7 + 86679x^6 - 26432x^5 + 14707x^4 - 1397x^3 + 132x^2 - 12x + 1	$40$	[0,20]	$3^{20}\cdot 5^{30}\cdot 11^{36}$	$3$	$50.1235182543$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	$[2, 4210]$	$10$	$19$	$276594299286030.2$
40.0.100...625.2	x^40 - x^39 + 5x^38 - 5x^37 + 20x^36 - 19x^35 + 74x^34 - 65x^33 + 265x^32 - 210x^31 + 936x^30 - 1475x^29 + 4114x^28 - 6060x^27 + 15680x^26 - 21989x^25 + 56355x^24 - 75531x^23 + 197315x^22 - 252030x^21 + 682811x^20 - 826140x^19 + 1114445x^18 - 1435731x^17 + 1906140x^16 - 2365144x^15 + 3132335x^14 - 3532620x^13 + 4695244x^12 - 3931240x^11 + 5449401x^10 + 1139235x^9 + 238165x^8 + 49790x^7 + 10409x^6 + 2176x^5 + 455x^4 + 95x^3 + 20x^2 + 4x + 1	$40$	[0,20]	$3^{20}\cdot 5^{30}\cdot 11^{36}$	$3$	$50.1235182543$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	not computed	$22$	$19$	$$
40.0.100...625.3	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	$40$	[0,20]	$3^{20}\cdot 5^{30}\cdot 11^{36}$	$3$	$50.1235182543$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	$[2, 9262]$	$6$	$19$	$60790762850097.93$
40.0.235...625.1	x^40 - x^38 - 8x^36 + 17x^34 + 55x^32 - 208x^30 - 287x^28 + 2159x^26 + 424x^24 - 19855x^22 + 16039x^20 - 178695x^18 + 34344x^16 + 1573911x^14 - 1883007x^12 - 12282192x^10 + 29229255x^8 + 81310473x^6 - 344373768x^4 - 387420489x^2 + 3486784401	$40$	[0,20]	$5^{20}\cdot 7^{20}\cdot 11^{36}$	$3$	$51.2020605454$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	not computed	$22$	$19$	$$
40.0.771...000.1	x^40 - 27x^38 + 452x^36 - 4707x^34 + 35613x^32 - 189939x^30 + 758623x^28 - 2202717x^26 + 4873258x^24 - 8161689x^22 + 10602647x^20 - 10506063x^18 + 8018080x^16 - 4542648x^14 + 1926084x^12 - 569703x^10 + 122757x^8 - 16992x^6 + 1555x^4 - 45x^2 + 1	$40$	[0,20]	$2^{40}\cdot 3^{20}\cdot 5^{20}\cdot 11^{32}$	$4$	$52.7460294983$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	$[341]$	$12$	$19$	$17492090815064632$
40.0.129...000.1	x^40 - 20x^38 + 230x^36 - 1800x^34 + 10625x^32 - 49003x^30 + 181750x^28 - 547185x^26 + 1349050x^24 - 2717025x^22 + 4465008x^20 - 5912800x^18 + 6247290x^16 - 5116175x^14 + 3173350x^12 - 1380878x^10 + 400970x^8 - 52915x^6 + 4850x^4 - 75x^2 + 1	$40$	[0,20]	$2^{40}\cdot 3^{20}\cdot 5^{68}$	$3$	$53.4367000111$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	$[11, 55]$	$12$	$19$	$12293887094064384$
40.0.204...561.1	x^40 - x^39 - 3x^38 + 10x^37 - 10x^36 - 30x^35 + 127x^34 - 127x^33 - 381x^32 + 1540x^31 - 1540x^30 + 5017x^29 + 9192x^28 - 47740x^27 + 39883x^26 + 133500x^25 - 518980x^24 + 534289x^23 + 1583184x^22 - 6478780x^21 + 6419731x^20 + 19436340x^19 + 14248656x^18 - 14425803x^17 - 42037380x^16 - 32440500x^15 + 29074707x^14 + 104407380x^13 + 60308712x^12 - 98749611x^11 - 90935460x^10 - 272806380x^9 - 202479021x^8 + 202479021x^7 + 607437063x^6 + 430467210x^5 - 430467210x^4 - 1291401630x^3 - 1162261467x^2 + 1162261467x + 3486784401	$40$	[0,20]	$3^{20}\cdot 11^{36}\cdot 13^{20}$	$3$	$54.0487581884$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	not computed	$66$	$19$	$$
40.0.280...496.1	x^40 + 257x^32 + 14016x^24 + 105419x^16 + 23219x^8 + 1	$40$	[0,20]	$2^{120}\cdot 11^{32}$	$2$	$54.4758650202$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	$[2605]$	$16$	$19$	$4506035972876552.0$
40.0.339...000.1	x^40 - 6x^38 + 32x^36 - 168x^34 + 880x^32 - 4608x^30 + 24128x^28 - 126336x^26 + 661504x^24 - 3463680x^22 + 18136064x^20 - 13854720x^18 + 10584064x^16 - 8085504x^14 + 6176768x^12 - 4718592x^10 + 3604480x^8 - 2752512x^6 + 2097152x^4 - 1572864x^2 + 1048576	$40$	[0,20]	$2^{60}\cdot 5^{20}\cdot 11^{36}$	$3$	$54.7373051594$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	not computed	$22$	$19$	$$
40.0.339...000.2	x^40 + 6x^38 + 32x^36 + 168x^34 + 880x^32 + 4608x^30 + 24128x^28 + 126336x^26 + 661504x^24 + 3463680x^22 + 18136064x^20 + 13854720x^18 + 10584064x^16 + 8085504x^14 + 6176768x^12 + 4718592x^10 + 3604480x^8 + 2752512x^6 + 2097152x^4 + 1572864x^2 + 1048576	$40$	[0,20]	$2^{60}\cdot 5^{20}\cdot 11^{36}$	$3$	$54.7373051594$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	not computed	$22$	$19$	$$
40.0.569...625.1	x^40 - 31x^35 + 718x^30 - 14725x^25 + 282001x^20 - 3578175x^15 + 42397182x^10 - 444816117x^5 + 3486784401	$40$	[0,20]	$5^{70}\cdot 11^{20}$	$2$	$55.4490168449$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	not computed	$50$	$19$	$$
40.0.316...000.1	x^40 + 41x^38 + 778x^36 + 9065x^34 + 72556x^32 + 422839x^30 + 1855505x^28 + 6253910x^26 + 16367625x^24 + 33406879x^22 + 53106978x^20 + 65321146x^18 + 61394717x^16 + 43240794x^14 + 22168369x^12 + 7925719x^10 + 1852081x^8 + 255047x^6 + 17190x^4 + 360x^2 + 1	$40$	[0,20]	$2^{40}\cdot 5^{30}\cdot 11^{36}$	$3$	$57.8776535137$	✓	✓	✓	$C_2\times C_{20}$ (as 40T2)	$[2, 85622]$	$4$	$19$	$60790762850097.93$
40.40.316...000.1	x^40 - 39x^38 + 702x^36 - 7735x^34 + 58344x^32 - 319177x^30 + 1308973x^28 - 4102514x^26 + 9927425x^24 - 18613969x^22 + 26988270x^20 - 30037766x^18 + 25334997x^16 - 15882694x^14 + 7199257x^12 - 2269345x^10 + 470613x^8 - 59241x^6 + 4018x^4 - 120x^2 + 1	$40$	[40,0]	$2^{40}\cdot 5^{30}\cdot 11^{36}$	$3$	$57.8776535137$		✓	✓	$C_2\times C_{20}$ (as 40T2)	trivial	$2$	$39$	$33894240488185236000000$
40.0.316...000.2	x^40 + 11x^38 + 77x^36 + 440x^34 + 2244x^32 + 9273x^30 + 33033x^28 + 104786x^26 + 294635x^24 + 688611x^22 + 1416910x^20 + 2574154x^18 + 3942422x^16 + 4573316x^14 + 4694437x^12 + 4152720x^10 + 2752508x^8 + 863819x^6 + 263538x^4 + 73205x^2 + 14641	$40$	[0,20]	$2^{40}\cdot 5^{30}\cdot 11^{36}$	$3$	$57.8776535137$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	not computed	$10$	$19$	$$
40.0.316...000.3	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	$40$	[0,20]	$2^{40}\cdot 5^{30}\cdot 11^{36}$	$3$	$57.8776535137$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	not computed	$22$	$19$	$$
40.0.324...000.1	x^40 + 40x^38 + 740x^36 + 8400x^34 + 65450x^32 + 371009x^30 + 1582270x^28 + 5178645x^26 + 13151125x^24 + 26030250x^22 + 40123776x^20 + 47888645x^18 + 43779420x^16 + 30152050x^14 + 15277900x^12 + 5507149x^10 + 1345115x^8 + 206465x^6 + 17450x^4 + 600x^2 + 1	$40$	[0,20]	$2^{40}\cdot 3^{20}\cdot 5^{70}$	$3$	$57.9146092644$	✓	✓	✓	$C_2\times C_{20}$ (as 40T2)	$[237710]$	$4$	$19$	$64293715230028.38$
40.40.324...000.1	x^40 - 40x^38 + 740x^36 - 8400x^34 + 65450x^32 - 371007x^30 + 1582210x^28 - 5177835x^26 + 13144625x^24 - 25995750x^22 + 39996264x^20 - 47552155x^18 + 43139880x^16 - 29279950x^14 + 14438100x^12 - 4952883x^10 + 1106455x^8 - 144655x^6 + 9150x^4 - 200x^2 + 1	$40$	[40,0]	$2^{40}\cdot 3^{20}\cdot 5^{70}$	$3$	$57.9146092644$		✓	✓	$C_2\times C_{20}$ (as 40T2)	trivial	$2$	$39$	$31857175264724490000000$
40.0.324...000.2	x^40 + 20x^38 + 230x^36 + 1800x^34 + 10625x^32 + 49005x^30 + 181750x^28 + 546975x^26 + 1346750x^24 + 2703375x^22 + 4412520x^20 + 5771300x^18 + 5985150x^16 + 4782125x^14 + 2915250x^12 + 1285650x^10 + 409750x^8 + 82625x^6 + 11250x^4 + 625x^2 + 25	$40$	[0,20]	$2^{40}\cdot 3^{20}\cdot 5^{70}$	$3$	$57.9146092644$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	not computed	$6$	$19$	$$
40.0.324...000.3	x^40 + 243x^30 + 59049x^20 + 14348907x^10 + 3486784401	$40$	[0,20]	$2^{40}\cdot 3^{20}\cdot 5^{70}$	$3$	$57.9146092644$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	not computed	$50$	$19$	$$
40.0.401...664.1	x^40 - 4x^38 + 14x^36 - 48x^34 + 164x^32 - 560x^30 + 1912x^28 - 6528x^26 + 22288x^24 - 76096x^22 + 259808x^20 - 152192x^18 + 89152x^16 - 52224x^14 + 30592x^12 - 17920x^10 + 10496x^8 - 6144x^6 + 3584x^4 - 2048x^2 + 1024	$40$	[0,20]	$2^{110}\cdot 11^{36}$	$2$	$58.2218370878$	✓	✓		$C_2\times C_{20}$ (as 40T2)	$[5731]$	$22$	$19$	$59973097516991576$
40.0.401...664.2	x^40 + 4x^38 + 14x^36 + 48x^34 + 164x^32 + 560x^30 + 1912x^28 + 6528x^26 + 22288x^24 + 76096x^22 + 259808x^20 + 152192x^18 + 89152x^16 + 52224x^14 + 30592x^12 + 17920x^10 + 10496x^8 + 6144x^6 + 3584x^4 + 2048x^2 + 1024	$40$	[0,20]	$2^{110}\cdot 11^{36}$	$2$	$58.2218370878$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	not computed	$22$	$19$	$$
40.0.445...000.1	x^40 - 3x^20 + 3	$40$	[0,20]	$2^{80}\cdot 3^{39}\cdot 5^{40}$	$3$	$58.3745060922$			✓	40T523	not computed	$6$	$19$	$$
40.0.673...721.1	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	$40$	[0,20]	$3^{20}\cdot 41^{38}$	$2$	$58.9800710306$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	$[8, 8, 8, 136]$	$6$	$19$	$310417721980536.1$
40.0.809...689.1	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	$40$	[0,20]	$11^{36}\cdot 13^{30}$	$2$	$59.2530801083$	✓	✓	not computed	$C_2\times C_{20}$ (as 40T2)	$[1525]$	$22$	$19$	$44099133482673080$
40.0.130...936.1	x^40 - 20x^38 + 231x^36 - 1812x^34 + 10709x^32 - 49280x^30 + 181674x^28 - 540148x^26 + 1304886x^24 - 2544812x^22 + 3994121x^20 - 4954644x^18 + 4817692x^16 - 3548680x^14 + 1959963x^12 - 753104x^10 + 202622x^8 - 30356x^6 + 3025x^4 - 60x^2 + 1	$40$	[0,20]	$2^{80}\cdot 3^{20}\cdot 11^{36}$	$3$	$59.9617135457$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	$[22, 110]$	$6$	$19$	$25665787785126296$
40.40.130...936.1	x^40 - 40x^38 + 741x^36 - 8436x^34 + 66044x^32 - 376960x^30 + 1622694x^28 - 5375528x^26 + 13860054x^24 - 27947920x^22 + 44043506x^20 - 53927016x^18 + 50713585x^16 - 35964944x^14 + 18713229x^12 - 6857500x^10 + 1662386x^8 - 240976x^6 + 17560x^4 - 480x^2 + 1	$40$	[40,0]	$2^{80}\cdot 3^{20}\cdot 11^{36}$	$3$	$59.9617135457$		✓	✓	$C_2^2\times C_{10}$ (as 40T7)	trivial	$2$	$39$	$73555688392588420000000$
40.0.130...936.2	x^40 - 4x^38 + 15x^36 - 56x^34 + 209x^32 - 780x^30 + 2911x^28 - 10864x^26 + 40545x^24 - 151316x^22 + 564719x^20 - 151316x^18 + 40545x^16 - 10864x^14 + 2911x^12 - 780x^10 + 209x^8 - 56x^6 + 15x^4 - 4x^2 + 1	$40$	[0,20]	$2^{80}\cdot 3^{20}\cdot 11^{36}$	$3$	$59.9617135457$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	$[5, 10, 110]$	$22$	$19$	$24039412784024376$
40.0.130...936.3	x^40 + 57x^36 + 1280x^32 + 14374x^28 + 85046x^24 + 259698x^20 + 379157x^16 + 222625x^12 + 41990x^8 + 820x^4 + 1	$40$	[0,20]	$2^{80}\cdot 3^{20}\cdot 11^{36}$	$3$	$59.9617135457$	✓	✓	not computed	$C_2^2\times C_{10}$ (as 40T7)	$[110, 110]$	$4$	$19$	$1535102994471753.0$