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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 20.0.6113193735657808322804901216256.3 | x20 + 20x18 + 169x16 + 784x14 + 2172x12 + 3664x10 + 3683x8 + 2072x6 + 575x4 + 60x2 + 1 | \( 2^{40}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[110]$ (GRH) |
| 20.0.13446022833304013177802344559616.1 | x20 + 36x18 + 571x16 + 5239x14 + 30667x12 + 118956x10 + 306783x8 + 511119x6 + 509969x4 + 254131x2 + 34429 | \( 2^{10}\cdot 11^{16}\cdot 43^{2}\cdot 67^{2}\cdot 34429 \) | 20T846 | $[2, 52]$ (GRH) |
| 20.0.43385989592539284614329771491328.1 | x20 + 23x18 + 228x16 + 1277x14 + 4449x12 + 9995x10 + 14495x8 + 13146x6 + 6875x4 + 1703x2 + 97 | \( 2^{20}\cdot 37^{2}\cdot 47^{2}\cdot 97\cdot 239^{2}\cdot 1571417^{2} \) | 20T1110 | $[156]$ (GRH) |
| 20.0.52105667456282068186172666015625.1 | x20 - 10x19 + 69x18 - 336x17 + 1320x16 - 4236x15 + 11537x14 - 26825x13 + 54035x12 - 94409x11 + 143761x10 - 190217x9 + 218312x8 - 215573x7 + 181526x6 - 128193x5 + 74327x4 - 34117x3 + 11742x2 - 2714x + 331 | \( 3^{4}\cdot 5^{10}\cdot 2251^{2}\cdot 23459^{2}\cdot 23622721 \) | 20T1045 | $[104]$ (GRH) |
| 20.0.56933553290160450365440000000000.1 | x20 + 17x18 + 124x16 + 502x14 + 1230x12 + 1858x10 + 1721x8 + 833x6 + 554x4 - 1560x2 + 7921 | \( 2^{20}\cdot 5^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[124]$ (GRH) |
| 20.0.56933553290160450365440000000000.3 | x20 - 5x18 + 25x16 - 125x14 + 625x12 - 3125x10 + 15625x8 - 78125x6 + 390625x4 - 1953125x2 + 9765625 | \( 2^{20}\cdot 5^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[2, 62]$ (GRH) |
| 20.0.92738759037689478010716606945681.3 | x20 - 8x19 + 27x18 - 52x17 + 132x16 - 452x15 + 1108x14 - 1974x13 + 4254x12 - 9042x11 + 17084x10 - 27764x9 + 50255x8 - 71930x7 + 123807x6 - 139074x5 + 238062x4 - 158880x3 + 351000x2 - 96318x + 278653 | \( 3^{10}\cdot 7^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[330]$ (GRH) |
| 20.0.112731072674656014761673622552576.1 | x20 + 44x18 + 546x16 + 2906x14 + 7573x12 + 10341x10 + 7573x8 + 2906x6 + 546x4 + 44x2 + 1 | \( 2^{20}\cdot 401^{10} \) | $D_{10}$ (as 20T4) | $[5, 50]$ (GRH) |
| 20.0.119528305286560475701940577107968.1 | x20 + 24x18 + 250x16 + 1481x14 + 5491x12 + 13208x10 + 20658x8 + 20459x6 + 12048x4 + 3708x2 + 433 | \( 2^{20}\cdot 433\cdot 460181^{2}\cdot 1114969^{2} \) | 20T1110 | $[340]$ (GRH) |
| 20.0.126754505709914865311944228515625.3 | x20 - 8x19 + 21x18 - 57x16 - 166x15 + 1385x14 - 3815x13 + 8065x12 - 16253x11 + 38496x10 - 88398x9 + 203504x8 - 392889x7 + 695944x6 - 1005043x5 + 1343738x4 - 1372952x3 + 1330894x2 - 768615x + 512579 | \( 5^{10}\cdot 7^{10}\cdot 11^{16} \) | $C_2\times C_{10}$ (as 20T3) | $[5, 55]$ (GRH) |
| 20.0.164422235102392733097076416015625.1 | x20 + 30x18 + 435x16 - 11x15 + 3750x14 - 265x13 + 20825x12 - 2735x11 + 74975x10 - 15000x9 + 173240x8 - 42800x7 + 238320x6 - 63648x5 + 172800x4 - 28800x3 + 32000x2 + 2560x + 1024 | \( 5^{34}\cdot 7^{10} \) | $C_2\times C_{10}$ (as 20T3) | $[4, 4, 4, 4]$ (GRH) |
| 20.0.175563371587677622582606371487744.1 | x20 + 24x18 + 247x16 + 1433x14 + 5173x12 + 12084x10 + 18387x8 + 17865x6 + 10523x4 + 3365x2 + 439 | \( 2^{20}\cdot 11^{16}\cdot 43^{2}\cdot 67^{2}\cdot 439 \) | 20T846 | $[2, 200]$ (GRH) |
| 20.0.211271772969714308085760000000000.1 | x20 + 29x18 + 320x16 + 1804x14 + 5753x12 + 10700x10 + 11469x8 + 6802x6 + 2144x4 + 330x2 + 19 | \( 2^{20}\cdot 5^{10}\cdot 19^{5}\cdot 1699^{4} \) | 20T168 | $[178]$ (GRH) |
| 20.0.211300041885398707129826254258176.1 | x20 + 24x18 + 234x16 + 1222x14 + 3778x12 + 7176x10 + 8348x8 + 5683x6 + 2014x4 + 272x2 + 1 | \( 2^{20}\cdot 3^{4}\cdot 61^{2}\cdot 401^{8} \) | 20T412 | $[120]$ (GRH) |
| 20.0.211505645444809969257911648518144.1 | x20 + 22x18 + 190x16 + 841x14 + 2109x12 + 3114x10 + 2698x8 + 1310x6 + 320x4 + 31x2 + 1 | \( 2^{20}\cdot 61^{6}\cdot 397^{6} \) | 20T281 | $[2, 90]$ (GRH) |
| 20.0.278769409858424250725488500146176.1 | x20 - 8x18 + 180x16 - 712x14 + 7134x12 - 5112x10 + 15140x8 - 99224x6 + 227145x4 - 91552x2 + 12544 | \( 2^{20}\cdot 439^{10} \) | $D_{10}$ (as 20T4) | $[5, 75]$ (GRH) |
| 20.0.352517555563337816067682238201856.2 | x20 + 38x18 + 608x16 + 5328x14 + 27872x12 + 89024x10 + 170560x8 + 184704x6 + 99840x4 + 20480x2 + 1024 | \( 2^{30}\cdot 3^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[5, 110]$ (GRH) |
| 20.0.352517555563337816067682238201856.5 | x20 + 22x18 + 308x16 + 2640x14 + 16544x12 + 70048x10 + 216832x8 + 418176x6 + 557568x4 + 309760x2 + 123904 | \( 2^{30}\cdot 3^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[124]$ (GRH) |
| 20.0.352517555563337816067682238201856.7 | x20 - 2x19 + x18 + 4x17 + 66x16 - 144x15 + 266x14 - 100x13 + 1822x12 - 3344x11 + 10198x10 - 10362x9 + 36517x8 - 42190x7 + 138157x6 - 145432x5 + 383064x4 - 352162x3 + 765484x2 - 438908x + 652081 | \( 2^{30}\cdot 3^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[2, 310]$ (GRH) |
| 20.0.352517555563337816067682238201856.9 | x20 + 6x18 + 36x16 + 216x14 + 1296x12 + 7776x10 + 46656x8 + 279936x6 + 1679616x4 + 10077696x2 + 60466176 | \( 2^{30}\cdot 3^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[124]$ (GRH) |
| 20.0.374049460594333053432589974619761.1 | x20 - 3x19 + 30x18 - 49x17 + 479x16 - 700x15 + 4546x14 - 4405x13 + 26875x12 - 26202x11 + 94832x10 - 61853x9 + 183245x8 - 143454x7 + 188321x6 - 72035x5 + 50332x4 - 16237x3 + 9324x2 - 2047x + 529 | \( 3^{10}\cdot 11^{16}\cdot 13^{10} \) | $C_2\times C_{10}$ (as 20T3) | $[110]$ (GRH) |
| 20.0.382427325615169748862424594776064.1 | x20 + 140x16 + 2560x12 + 9316x8 + 8944x4 + 64 | \( 2^{26}\cdot 11^{8}\cdot 113^{8} \) | 20T230 | $[2, 70]$ (GRH) |
| 20.0.415282752787656250000000000000000.1 | x20 - 5x18 - 15x16 - 60x15 + 90x14 + 200x13 + 655x12 + 3020x11 + 1117x10 - 3050x9 + 29145x8 + 82980x7 + 68790x6 + 42730x5 + 171825x4 + 442940x3 + 629335x2 + 483750x + 162871 | \( 2^{16}\cdot 5^{22}\cdot 7^{10}\cdot 97^{2} \) | 20T140 | $[156]$ (GRH) |
| 20.0.463378613159711142474292153810944.1 | x20 + 22x18 + 202x16 + 1005x14 + 2937x12 + 5095x10 + 5027x8 + 2523x6 + 519x4 + 41x2 + 1 | \( 2^{20}\cdot 3^{2}\cdot 271^{2}\cdot 401^{8} \) | 20T412 | $[3, 120]$ (GRH) |
| 20.0.481817839414250422927360000000000.3 | x20 - 2x19 - 5x18 + 6x17 + 79x16 - 66x15 + 322x14 - 536x13 + 3374x12 - 3100x11 + 19969x10 - 5580x9 + 93762x8 - 1416x7 + 311223x6 + 38138x5 + 714780x4 + 78782x3 + 1041689x2 + 24970x + 767371 | \( 2^{30}\cdot 5^{10}\cdot 11^{16} \) | $C_2\times C_{10}$ (as 20T3) | $[5, 155]$ (GRH) |
| 20.0.485922591755172262707200000000000.1 | x20 + 25x18 + 247x16 + 1290x14 + 3953x12 + 7365x10 + 8267x8 + 5270x6 + 1641x4 + 165x2 + 5 | \( 2^{36}\cdot 5^{11}\cdot 3469^{4} \) | 20T755 | $[170]$ (GRH) |
| 20.0.625000000000000000000000000000000.1 | x20 + 40x18 + 680x16 + 6400x14 + 36400x12 + 128096x10 + 273920x8 + 333440x6 + 198400x4 + 38400x2 + 1024 | \( 2^{30}\cdot 5^{34} \) | $C_2\times C_{10}$ (as 20T3) | $[451]$ (GRH) |
| 20.0.706388839731582814105670315409408.1 | x20 - 8x19 + 48x18 - 194x17 + 657x16 - 1808x15 + 4398x14 - 9430x13 + 18493x12 - 33000x11 + 56352x10 - 91110x9 + 153485x8 - 242326x7 + 407778x6 - 515444x5 + 857558x4 - 668326x3 + 1079706x2 - 137098x + 8641 | \( 2^{30}\cdot 3^{15}\cdot 71^{9} \) | $C_5\times C_5:D_4$ (as 20T53) | $[2, 82]$ (GRH) |
| 20.0.733010848644118650331248974626816.1 | x20 - 3x18 + 18x16 + 184x14 + 15x12 + 441x10 + 1587x8 - 5372x6 + 5879x4 - 2750x2 + 625 | \( 2^{20}\cdot 31^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[123]$ (GRH) |
| 20.0.819763362363033867895669628338176.1 | x20 - 14x18 + 167x16 - 780x14 + 2015x12 + 11490x10 - 72343x8 + 144184x6 - 155888x4 + 61440x2 + 147456 | \( 2^{20}\cdot 3^{10}\cdot 163^{10} \) | $D_{10}$ (as 20T4) | $[11, 22]$ (GRH) |
| 20.0.819763362363033867895669628338176.2 | x20 - 234x16 - 1208x14 + 14355x12 + 160128x10 + 603766x8 + 1060704x6 + 977697x4 + 835704x2 + 352836 | \( 2^{20}\cdot 3^{10}\cdot 163^{10} \) | $D_{10}$ (as 20T4) | $[11, 22]$ (GRH) |
| 20.0.819763362363033867895669628338176.3 | x20 - 18x18 + 83x16 - 12x14 + 357x12 - 3306x10 + 2885x8 + 36816x6 - 21389x4 - 274590x2 + 622521 | \( 2^{20}\cdot 3^{10}\cdot 163^{10} \) | $D_{10}$ (as 20T4) | $[11, 22]$ (GRH) |
| 20.0.1004734915970976698000000000000000.1 | x20 - 2x19 + 27x18 - 50x17 + 249x16 - 570x15 + 1254x14 - 3934x13 + 6887x12 - 13648x11 + 30841x10 - 44850x9 + 78071x8 - 119082x7 + 145974x6 - 178652x5 + 172159x4 - 56358x3 + 212471x2 + 51356x + 99301 | \( 2^{16}\cdot 5^{15}\cdot 3469^{5} \) | $D_5^2:C_4$ (as 20T94) | $[2, 4, 36]$ (GRH) |
| 20.0.1059431841229213450878936767578125.1 | x20 + 9x18 - 20x17 + 75x16 - 180x15 + 861x14 - 2865x13 + 7959x12 - 15010x11 + 22236x10 - 24435x9 + 23095x8 - 18390x7 + 16869x6 - 13500x5 + 12456x4 - 9315x3 + 7560x2 - 4050x + 2025 | \( 3^{16}\cdot 5^{15}\cdot 73^{8} \) | $C_4\times A_5$ (as 20T63) | $[2, 68]$ (GRH) |
| 20.0.1069756574259831337445098876953125.1 | x20 + 22x18 - 8x17 + 207x16 - 159x15 + 1229x14 - 1352x13 + 5527x12 - 6687x11 + 19563x10 - 26099x9 + 61052x8 - 84787x7 + 142519x6 - 138535x5 + 133978x4 - 34522x3 - 24228x2 + 24879x + 22171 | \( 5^{15}\cdot 19^{5}\cdot 1699^{5} \) | $D_5^2:C_4$ (as 20T94) | $[6, 60]$ (GRH) |
| 20.0.1262666518217374016383382656250000.1 | x20 - 5x19 + 29x18 - 99x17 + 350x16 - 953x15 + 2527x14 - 5606x13 + 11829x12 - 20902x11 + 35258x10 - 48172x9 + 69054x8 - 82765x7 + 123756x6 - 157517x5 + 218213x4 - 212875x3 + 178015x2 - 76246x + 23209 | \( 2^{4}\cdot 5^{10}\cdot 52501^{4}\cdot 1063649 \) | 20T876 | $[218]$ (GRH) |
| 20.0.1307963560411124698019840000000000.1 | x20 + 37x18 + 545x16 + 4213x14 + 19106x12 + 53478x10 + 93622x8 + 100350x6 + 61380x4 + 17908x2 + 1331 | \( 2^{20}\cdot 5^{10}\cdot 11^{5}\cdot 28162171^{2} \) | 20T781 | $[2, 450]$ (GRH) |
| 20.0.1311120134664566839939604313800704.1 | x20 + 29x18 + 329x16 + 1917x14 + 6286x12 + 11958x10 + 13162x8 + 8124x6 + 2583x4 + 335x2 + 4 | \( 2^{32}\cdot 83^{6}\cdot 983^{4} \) | 20T994 | $[2, 86]$ (GRH) |
| 20.0.1316926149061478577602560000000000.1 | x20 - 10x19 + 59x18 - 216x17 + 521x16 - 808x15 + 894x14 - 1546x13 + 4905x12 - 8670x11 + 5177x10 + 7432x9 - 18513x8 - 19136x7 + 21318x6 - 30316x5 + 268819x4 + 16550x3 + 337065x2 + 37050x + 94025 | \( 2^{28}\cdot 5^{10}\cdot 3469^{5} \) | $C_2\times D_5\wr C_2$ (as 20T92) | $[198]$ (GRH) |
| 20.0.1368208637864347439721375491751936.1 | x20 - 5x19 + 16x18 + 3x17 + 57x16 - 202x15 + 43x14 - 817x13 + 2557x12 - 1698x11 - 1837x10 + 5343x9 - 4748x8 - 3541x7 + 14483x6 - 5772x5 + 6580x4 + 6848x3 + 192x2 - 2048x + 1024 | \( 2^{16}\cdot 3^{2}\cdot 41^{2}\cdot 53^{14} \) | 20T140 | $[120]$ (GRH) |
| 20.0.1378292916885385650670001824763904.1 | x20 + 14x18 + 135x16 + 660x14 + 2317x12 + 4630x10 + 6589x8 + 4340x6 + 2019x4 + 46x2 + 1 | \( 2^{12}\cdot 3^{10}\cdot 11^{8}\cdot 113^{8} \) | 20T230 | $[6, 18]$ (GRH) |
| 20.0.1465621300755332525247833251953125.1 | x20 - 3x19 + 13x18 - 45x17 + 181x16 - 277x15 + 1527x14 - 1917x13 + 6069x12 - 8567x11 + 22087x10 + 8548x9 + 131627x8 + 225444x7 + 530121x6 + 803419x5 + 996120x4 + 1044920x3 + 674906x2 + 243078x + 96739 | \( 5^{15}\cdot 6029^{6} \) | 20T369 | $[2, 212]$ (GRH) |
| 20.0.1646829531350307068613612031442944.1 | x20 + 43x18 + 793x16 + 8183x14 + 51657x12 + 204599x10 + 500105x8 + 707959x6 + 500105x4 + 119415x2 + 4489 | \( 2^{20}\cdot 7^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[124]$ (GRH) |
| 20.0.1646829531350307068613612031442944.3 | x20 - 10x19 + 43x18 - 102x17 + 208x16 - 644x15 + 1932x14 - 3886x13 + 6858x12 - 15070x11 + 32440x10 - 52602x9 + 84390x8 - 144344x7 + 228417x6 - 279504x5 + 404164x4 - 466344x3 + 532837x2 - 328784x + 558097 | \( 2^{20}\cdot 7^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[2, 310]$ (GRH) |
| 20.0.1646829531350307068613612031442944.4 | x20 + 7x18 + 49x16 + 343x14 + 2401x12 + 16807x10 + 117649x8 + 823543x6 + 5764801x4 + 40353607x2 + 282475249 | \( 2^{20}\cdot 7^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[124]$ (GRH) |
| 20.0.1655513490330868290261743826894848.1 | x20 + 36x18 + 498x16 + 3416x14 + 12736x12 + 26944x10 + 32408x8 + 21280x6 + 6960x4 + 960x2 + 32 | \( 2^{55}\cdot 11^{16} \) | $C_{20}$ (as 20T1) | $[521]$ (GRH) |
| 20.0.2131588214553606414985382080078125.1 | x20 - 5x19 + 13x18 - 17x17 + 94x16 - 151x15 + 406x14 - 633x13 + 3653x12 - 772x11 + 13426x10 + 5719x9 + 24764x8 + 15388x7 + 21892x6 + 15269x5 + 9379x4 + 3157x3 + 732x2 - 45x + 1 | \( 3^{8}\cdot 5^{15}\cdot 239^{8} \) | $C_4\times D_5$ (as 20T6) | $[2, 58]$ (GRH) |
| 20.0.2339097430337203010794683455827681.1 | x20 - x19 + 8x18 - 15x17 + 71x16 - 176x15 + 673x14 - 1905x13 + 6616x12 - 19951x11 + 66263x10 + 139657x9 + 324184x8 + 653415x7 + 1615873x6 + 2958032x5 + 8353079x4 + 12353145x3 + 46118408x2 + 40353607x + 282475249 | \( 11^{18}\cdot 29^{10} \) | $C_2\times C_{10}$ (as 20T3) | $[275]$ (GRH) |
| 20.0.2429612958775861313536000000000000.1 | x20 + 27x18 + 285x16 + 1526x14 + 4591x12 + 8189x10 + 8821x8 + 5660x6 + 2055x4 + 375x2 + 25 | \( 2^{36}\cdot 5^{12}\cdot 3469^{4} \) | 20T760 | $[448]$ (GRH) |
| 20.0.2429612958775861313536000000000000.2 | x20 + 29x18 + 343x16 + 2140x14 + 7593x12 + 15429x10 + 17441x8 + 10620x6 + 3295x4 + 475x2 + 25 | \( 2^{36}\cdot 5^{12}\cdot 3469^{4} \) | 20T760 | $[432]$ (GRH) |
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