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Label Polynomial Discriminant Galois group Class group
20.0.291...125.1 x20 - x15 + x10 - x5 + 1 \( 5^{35} \) $C_{20}$ (as 20T1) trivial
20.0.140...125.1 x20 - x19 + 5x18 - 6x17 + 20x16 - 11x15 + 59x14 - 30x13 + 179x12 - 109x11 + 260x10 - 128x9 + 334x8 + 82x7 + 199x6 + 22x5 + 146x4 - 41x3 + 12x2 - 3x + 1 \( 5^{15}\cdot 11^{16} \) $C_{20}$ (as 20T1) $[5]$
20.20.169...125.1 x20 - x19 - 20x18 + 19x17 + 170x16 - 151x15 - 801x14 + 650x13 + 2289x12 - 1639x11 - 4080x10 + 2442x9 + 4489x8 - 2058x7 - 2891x6 + 877x5 + 951x4 - 151x3 - 108x2 + 12x + 1 \( 5^{15}\cdot 11^{18} \) $C_{20}$ (as 20T1) trivial (GRH)
20.20.171...125.1 x20 - 20x18 + 170x16 - x15 - 800x14 + 15x13 + 2275x12 - 90x11 - 4004x10 + 275x9 + 4290x8 - 450x7 - 2640x6 + 379x5 + 825x4 - 145x3 - 100x2 + 20x + 1 \( 3^{10}\cdot 5^{35} \) $C_{20}$ (as 20T1) trivial (GRH)
20.20.305...000.1 x20 - 20x18 + 170x16 - 800x14 + 2275x12 - 4005x10 + 4300x8 - 2675x6 + 875x4 - 125x2 + 5 \( 2^{20}\cdot 5^{35} \) $C_{20}$ (as 20T1) trivial (GRH)
20.20.439...361.1 x20 - x19 - 19x18 + 18x17 + 153x16 - 136x15 - 680x14 + 560x13 + 1820x12 - 1365x11 - 3003x10 + 2002x9 + 3003x8 - 1716x7 - 1716x6 + 792x5 + 495x4 - 165x3 - 55x2 + 10x + 1 \( 41^{19} \) $C_{20}$ (as 20T1) trivial (GRH)
20.20.828...125.1 x20 - x19 - 39x18 + 43x17 + 579x16 - 664x15 - 4199x14 + 4764x13 + 16062x12 - 17268x11 - 32674x10 + 31502x9 + 34487x8 - 26929x7 - 18180x6 + 9222x5 + 4671x4 - 978x3 - 468x2 - 21x + 1 \( 3^{10}\cdot 5^{15}\cdot 11^{16} \) $C_{20}$ (as 20T1) trivial (GRH)
20.20.822...125.1 x20 - 40x18 + 680x16 - 11x15 - 6400x14 + 330x13 + 36400x12 - 3960x11 - 128039x10 + 24200x9 + 272780x8 - 79200x7 - 325460x6 + 132429x5 + 175600x4 - 92290x3 - 15600x2 + 8580x + 401 \( 5^{35}\cdot 7^{10} \) $C_{20}$ (as 20T1) trivial (GRH)
20.20.147...000.1 x20 - 4x19 - 35x18 + 146x17 + 455x16 - 2044x15 - 2696x14 + 13960x13 + 6764x12 - 48836x11 - 2270x10 + 84688x9 - 15516x8 - 65992x7 + 17949x6 + 20748x5 - 6419x4 - 1814x3 + 787x2 - 72x + 1 \( 2^{20}\cdot 5^{15}\cdot 11^{16} \) $C_{20}$ (as 20T1) trivial (GRH)
20.0.165...848.1 x20 + 36x18 + 498x16 + 3416x14 + 12736x12 + 26944x10 + 32408x8 + 21280x6 + 6960x4 + 960x2 + 32 \( 2^{55}\cdot 11^{16} \) $C_{20}$ (as 20T1) $[521]$ (GRH)
20.20.165...848.1 x20 - 36x18 + 498x16 - 3416x14 + 12736x12 - 26944x10 + 32408x8 - 21280x6 + 6960x4 - 960x2 + 32 \( 2^{55}\cdot 11^{16} \) $C_{20}$ (as 20T1) trivial (GRH)
20.0.235...877.1 x20 - x19 - 9x18 + 31x17 + 55x16 - 48x15 + 189x14 + 352x13 + 1680x12 + 4302x11 + 4614x10 + 17042x9 + 24675x8 + 19061x7 + 33622x6 - 55350x5 - 15945x4 + 101736x3 + 82138x2 - 16471x + 40283 \( 11^{16}\cdot 13^{15} \) $C_{20}$ (as 20T1) $[61]$ (GRH)
20.0.312...000.1 x20 + 40x18 + 680x16 + 6400x14 + 36400x12 + 128160x10 + 275200x8 + 342400x6 + 224000x4 + 64000x2 + 5120 \( 2^{30}\cdot 5^{35} \) $C_{20}$ (as 20T1) $[1202]$ (GRH)
20.20.312...000.1 x20 - 40x18 + 680x16 - 6400x14 + 36400x12 - 128160x10 + 275200x8 - 342400x6 + 224000x4 - 64000x2 + 5120 \( 2^{30}\cdot 5^{35} \) $C_{20}$ (as 20T1) trivial (GRH)
20.0.834...741.1 x20 - x19 + 2x18 + 36x17 - 29x16 + 51x15 + 413x14 - 267x13 + 414x12 + 1778x11 - 745x10 + 691x9 + 3278x8 - 541x7 - 1330x6 + 1820x5 - 261x4 - 439x3 + 2983x2 - 522x + 611 \( 61^{19} \) $C_{20}$ (as 20T1) $[41]$ (GRH)
20.0.100...125.1 x20 - x19 + 35x18 - 36x17 + 500x16 - 536x15 + 3874x14 - 4410x13 + 18734x12 - 23144x11 + 64285x10 - 88253x9 + 181094x8 - 254178x7 + 456689x6 - 492583x5 + 958226x4 - 411001x3 + 1371042x2 + 173262x + 1197901 \( 3^{10}\cdot 5^{15}\cdot 11^{18} \) $C_{20}$ (as 20T1) $[2, 2, 842]$ (GRH)
20.0.221...125.2 x20 - x19 + 13x18 - 4x17 + 138x16 - 481x15 + 2045x14 - 4980x13 + 19301x12 - 36325x11 + 68890x10 - 104714x9 + 174168x8 - 44226x7 + 47983x6 - 14164x5 + 10616x4 + 445x3 + 2650x2 - 125x + 625 \( 5^{15}\cdot 31^{16} \) $C_{20}$ (as 20T1) $[2, 2, 10, 10]$ (GRH)
20.20.754...125.1 x20 - 60x18 + 1530x16 - 31x15 - 21600x14 + 1395x13 + 184275x12 - 25110x11 - 972254x10 + 230175x9 + 3105870x8 - 1129950x7 - 5547510x6 + 2832749x5 + 4443525x4 - 2942985x3 - 514350x2 + 354330x + 51151 \( 5^{35}\cdot 11^{10} \) $C_{20}$ (as 20T1) trivial (GRH)
20.20.131...673.1 x20 - x19 - 49x18 + 32x17 + 926x16 - 354x15 - 8765x14 + 1660x13 + 45828x12 - 2629x11 - 137522x10 - 4409x9 + 237299x8 + 22455x7 - 226443x6 - 31515x5 + 107725x4 + 17397x3 - 20309x2 - 2449x + 1033 \( 11^{16}\cdot 17^{15} \) $C_{20}$ (as 20T1) trivial (GRH)
20.0.177...000.1 x20 + 55x18 + 1265x16 + 15950x14 + 121550x12 + 581625x10 + 1754500x8 + 3251875x6 + 3478750x4 + 1890625x2 + 378125 \( 2^{20}\cdot 5^{15}\cdot 11^{18} \) $C_{20}$ (as 20T1) $[2, 2, 2762]$ (GRH)
20.0.180...000.1 x20 + 60x18 + 1530x16 + 21600x14 + 184275x12 + 973215x10 + 3134700x8 + 5850225x6 + 5740875x4 + 2460375x2 + 295245 \( 2^{20}\cdot 3^{10}\cdot 5^{35} \) $C_{20}$ (as 20T1) $[2, 4322]$ (GRH)
20.0.200...608.1 x20 + 44x18 + 770x16 + 6952x14 + 35552x12 + 107712x10 + 196504x8 + 212960x6 + 129712x4 + 38720x2 + 3872 \( 2^{55}\cdot 11^{18} \) $C_{20}$ (as 20T1) $[2050]$ (GRH)
20.20.200...608.1 x20 - 44x18 + 770x16 - 6952x14 + 35552x12 - 107712x10 + 196504x8 - 212960x6 + 129712x4 - 38720x2 + 3872 \( 2^{55}\cdot 11^{18} \) $C_{20}$ (as 20T1) trivial (GRH)
20.0.259...689.1 x20 - x19 + 22x18 - 23x17 + 153x16 - 177x15 + 304x14 - 506x13 - 476x12 + 316x11 - 1773x10 + 5692x9 - 8231x8 + 16816x7 + 2671x6 + 10386x5 + 74910x4 - 82739x3 + 50170x2 + 37115x + 51907 \( 3^{10}\cdot 41^{19} \) $C_{20}$ (as 20T1) $[2, 2, 2, 2, 34]$ (GRH)
20.20.284...117.1 x20 - x19 - 51x18 + 48x17 + 998x16 - 854x15 - 9572x14 + 7010x13 + 48842x12 - 27812x11 - 139547x10 + 54957x9 + 224814x8 - 51088x7 - 194675x6 + 16639x5 + 78872x4 + 1845x3 - 10254x2 - 1316x - 43 \( 11^{18}\cdot 13^{15} \) $C_{20}$ (as 20T1) trivial (GRH)
20.20.396...125.1 x20 - x19 - 64x18 + 78x17 + 1609x16 - 2224x15 - 20399x14 + 30774x13 + 139797x12 - 228288x11 - 510719x10 + 929822x9 + 878982x8 - 2003579x7 - 355510x6 + 2013497x5 - 574064x4 - 658628x3 + 441152x2 - 86946x + 4621 \( 5^{15}\cdot 7^{10}\cdot 11^{16} \) $C_{20}$ (as 20T1) trivial (GRH)
20.0.401...125.1 x20 + 60x18 + 1530x16 - 61x15 + 21600x14 - 2745x13 + 184275x12 - 49410x11 + 976936x10 - 452925x9 + 3246330x8 - 2223450x7 + 7022340x6 - 5859721x5 + 10764225x4 - 10075065x3 + 9995400x2 - 13549320x + 18662101 \( 5^{35}\cdot 13^{10} \) $C_{20}$ (as 20T1) $[15362]$ (GRH)
20.0.150...000.1 x20 - 4x19 + 40x18 - 124x17 + 815x16 - 2164x15 + 10834x14 - 24620x13 + 101774x12 - 198776x11 + 710860x10 - 1188452x9 + 3826719x8 - 5429272x7 + 15991074x6 - 18262392x5 + 47151361x4 - 38741504x3 + 92992732x2 - 43101732x + 90594151 \( 2^{30}\cdot 5^{15}\cdot 11^{16} \) $C_{20}$ (as 20T1) $[22082]$ (GRH)
20.20.150...000.2 x20 - 4x19 - 60x18 + 236x17 + 1435x16 - 5524x15 - 17726x14 + 66220x13 + 122474x12 - 437336x11 - 480740x10 + 1596028x9 + 1047359x8 - 3070872x7 - 1203606x6 + 2823768x5 + 614261x4 - 1007904x3 - 118608x2 + 70588x + 1451 \( 2^{30}\cdot 5^{15}\cdot 11^{16} \) $C_{20}$ (as 20T1) $[5]$ (GRH)
20.0.194...125.1 x20 - x19 + 17x18 - 38x17 + 294x16 + 679x15 + 3849x14 + 6496x13 + 45177x12 + 27901x11 + 73952x10 + 44804x9 + 108670x8 + 59106x7 + 153711x6 + 82674x5 + 202338x4 + 88695x3 + 39366x2 + 15309x + 6561 \( 5^{15}\cdot 41^{16} \) $C_{20}$ (as 20T1) $[505]$ (GRH)
20.0.460...936.1 x20 + 41x18 + 656x16 + 5289x14 + 23165x12 + 55801x10 + 71545x8 + 45141x6 + 13120x4 + 1517x2 + 41 \( 2^{20}\cdot 41^{19} \) $C_{20}$ (as 20T1) $[2, 482]$ (GRH)
20.0.586...125.1 x20 + 80x18 + 2720x16 - 101x15 + 51200x14 - 6060x13 + 582400x12 - 145440x11 + 4111321x10 - 1777600x9 + 18020840x8 - 11635200x7 + 49539760x6 - 40331421x5 + 89987200x4 - 82660420x3 + 98054400x2 - 123793680x + 161532401 \( 5^{35}\cdot 17^{10} \) $C_{20}$ (as 20T1) $[11, 5302]$ (GRH)
20.0.159...433.1 x20 - x19 + 27x18 - 31x17 + 348x16 - 472x15 + 2986x14 - 4874x13 + 20558x12 - 40054x11 + 130294x10 - 168519x9 + 700706x8 - 32881x7 + 2845143x6 + 2390937x5 + 8994354x4 + 9962701x3 + 26015925x2 + 20544384x + 83519437 \( 11^{18}\cdot 17^{15} \) $C_{20}$ (as 20T1) $[8194]$ (GRH)
20.20.178...125.1 x20 - 100x18 + 4250x16 - 101x15 - 100000x14 + 7575x13 + 1421875x12 - 227250x11 - 12505424x10 + 3471875x9 + 66677450x8 - 28406250x7 - 200058500x6 + 118907199x5 + 278040625x4 - 210961225x3 - 84750000x2 + 68478000x - 6502099 \( 5^{35}\cdot 19^{10} \) $C_{20}$ (as 20T1) trivial (GRH)
20.20.213...125.1 x20 - x19 - 57x18 + 66x17 + 1198x16 - 1526x15 - 12200x14 + 17240x13 + 64636x12 - 104480x11 - 174550x10 + 341431x9 + 205983x8 - 586336x7 - 12337x6 + 478381x5 - 146594x4 - 137680x3 + 63070x2 + 8405x - 4645 \( 5^{15}\cdot 31^{18} \) $C_{20}$ (as 20T1) trivial (GRH)
20.20.429...625.1 x20 - x19 - 60x18 + 59x17 + 1465x16 - 1407x15 - 18966x14 + 17616x13 + 142122x12 - 125226x11 - 630959x10 + 509336x9 + 1631687x8 - 1138974x7 - 2320717x6 + 1291062x5 + 1584530x4 - 656657x3 - 352368x2 + 129857x - 4099 \( 5^{10}\cdot 41^{19} \) $C_{20}$ (as 20T1) $[2]$ (GRH)
20.0.479...125.1 x20 - x19 + 90x18 - 91x17 + 3360x16 - 3451x15 + 68499x14 - 71950x13 + 849729x12 - 921679x11 + 6805360x10 - 7799638x9 + 36820719x8 - 45394658x7 + 141833529x6 - 176867903x5 + 410339451x4 - 382542201x3 + 863744092x2 - 219225038x + 1102456301 \( 5^{15}\cdot 7^{10}\cdot 11^{18} \) $C_{20}$ (as 20T1) $[2, 2, 64564]$ (GRH)
20.0.485...125.1 x20 + 100x18 + 4250x16 - 151x15 + 100000x14 - 11325x13 + 1421875x12 - 339750x11 + 12538426x10 - 5190625x9 + 68327550x8 - 42468750x7 + 228935250x6 - 182755451x5 + 484303125x4 - 439980025x3 + 600406250x2 - 725290750x + 924979351 \( 3^{10}\cdot 5^{35}\cdot 7^{10} \) $C_{20}$ (as 20T1) $[2, 2, 2, 2, 122, 122]$ (GRH)
20.0.868...000.3 x20 - 4x19 + 65x18 - 214x17 + 2035x16 - 5724x15 + 39824x14 - 96080x13 + 534824x12 - 1102236x11 + 5168310x10 - 9006872x9 + 36960084x8 - 53466672x7 + 196375269x6 - 224863132x5 + 733497061x4 - 597365054x3 + 1764047967x2 - 786154512x + 2065660201 \( 2^{20}\cdot 3^{10}\cdot 5^{15}\cdot 11^{16} \) $C_{20}$ (as 20T1) $[10, 31810]$ (GRH)
20.0.977...552.1 x20 - 4x19 + 50x18 - 160x17 + 1183x16 - 3204x15 + 16682x14 - 38000x13 + 149216x12 - 282888x11 + 886308x10 - 1402508x9 + 4088499x8 - 5786136x7 + 17951094x6 - 21370648x5 + 47163703x4 - 38829056x3 + 95586810x2 - 47685756x + 95829823 \( 2^{55}\cdot 3^{10}\cdot 11^{16} \) $C_{20}$ (as 20T1) $[131042]$ (GRH)
20.20.977...552.1 x20 - 4x19 - 70x18 + 272x17 + 1927x16 - 7236x15 - 27190x14 + 97888x13 + 215144x12 - 732552x11 - 977916x10 + 3078868x9 + 2504547x8 - 7029912x7 - 3351642x6 + 7942856x5 + 1920559x4 - 3602816x3 - 111054x2 + 391236x + 6247 \( 2^{55}\cdot 3^{10}\cdot 11^{16} \) $C_{20}$ (as 20T1) trivial (GRH)
20.20.120...125.1 x20 - 120x18 + 6120x16 - 151x15 - 172800x14 + 13590x13 + 2948400x12 - 489240x11 - 31120079x10 + 8969400x9 + 199252740x8 - 88063200x7 - 720099540x6 + 442743929x5 + 1223413200x4 - 953469870x3 - 520959600x2 + 437027220x - 64286399 \( 5^{35}\cdot 23^{10} \) $C_{20}$ (as 20T1) trivial (GRH)
20.0.120...901.1 x20 - x19 + 3x18 - 11x17 + 44x16 + 300x15 + 316x14 - 1991x13 - 80x12 + 1958x11 + 24000x10 + 7237x9 - 31618x8 - 6930x7 + 112662x6 + 144019x5 - 16152x4 - 21866x3 + 125333x2 + 197892x + 120577 \( 101^{19} \) $C_{20}$ (as 20T1) $[5, 25]$ (GRH)
20.20.138...973.1 x20 - x19 - 74x18 - 8x17 + 2161x16 + 2188x15 - 30387x14 - 53182x13 + 205169x12 + 517750x11 - 537473x10 - 2291342x9 - 343368x8 + 4213355x7 + 3433304x6 - 1687071x5 - 3020232x4 - 1007476x3 + 2500x2 + 17940x + 529 \( 3^{10}\cdot 11^{16}\cdot 13^{15} \) $C_{20}$ (as 20T1) trivial (GRH)
20.0.182...000.1 x20 + 110x18 + 5060x16 + 127600x14 + 1944800x12 + 18612000x10 + 112288000x8 + 416240000x6 + 890560000x4 + 968000000x2 + 387200000 \( 2^{30}\cdot 5^{15}\cdot 11^{18} \) $C_{20}$ (as 20T1) $[2, 2, 62564]$ (GRH)
20.20.182...000.1 x20 - 110x18 + 5060x16 - 127600x14 + 1944800x12 - 18612000x10 + 112288000x8 - 416240000x6 + 890560000x4 - 968000000x2 + 387200000 \( 2^{30}\cdot 5^{15}\cdot 11^{18} \) $C_{20}$ (as 20T1) $[2]$ (GRH)
20.0.184...000.1 x20 + 120x18 + 6120x16 + 172800x14 + 2948400x12 + 31142880x10 + 200620800x8 + 748828800x6 + 1469664000x4 + 1259712000x2 + 302330880 \( 2^{30}\cdot 3^{10}\cdot 5^{35} \) $C_{20}$ (as 20T1) $[2, 152842]$ (GRH)
20.20.184...000.1 x20 - 120x18 + 6120x16 - 172800x14 + 2948400x12 - 31142880x10 + 200620800x8 - 748828800x6 + 1469664000x4 - 1259712000x2 + 302330880 \( 2^{30}\cdot 3^{10}\cdot 5^{35} \) $C_{20}$ (as 20T1) $[2]$ (GRH)
20.0.193...125.1 x20 - x19 + 61x18 - 97x17 + 1959x16 - 3824x15 + 42001x14 - 86676x13 + 651922x12 - 1272388x11 + 7455206x10 - 12647278x9 + 61958107x8 - 85243529x7 + 364805340x6 - 374838878x5 + 1487095911x4 - 973042478x3 + 3808215652x2 - 1149290321x + 4751163121 \( 5^{15}\cdot 11^{16}\cdot 13^{10} \) $C_{20}$ (as 20T1) $[331922]$ (GRH)
20.0.396...789.1 x20 - x19 + x18 - 93x17 + 209x16 - 800x15 + 4981x14 - 12556x13 + 52672x12 - 186410x11 + 461402x10 - 1486634x9 + 3730667x8 - 7453323x7 + 16223240x6 - 23433182x5 + 16658019x4 - 7158636x3 + 5906450x2 - 2576267x + 1575113 \( 11^{16}\cdot 29^{15} \) $C_{20}$ (as 20T1) $[8221]$ (GRH)
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