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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 20.0.5969915757478328440239161344.6 | x20 + 2x18 + 4x16 + 8x14 + 16x12 + 32x10 + 64x8 + 128x6 + 256x4 + 512x2 + 1024 | \( 2^{30}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[11]$ |
| 20.0.15545170849776123808325331729.1 | x20 - 4x19 + 18x18 - 38x17 + 107x16 - 174x15 + 407x14 - 512x13 + 951x12 - 910x11 + 1518x10 - 1144x9 + 1544x8 - 787x7 + 959x6 - 418x5 + 294x4 - 42x3 + 18x2 + 1 | \( 3^{10}\cdot 460181^{2}\cdot 1114969^{2} \) | 20T1021 | $[11]$ (GRH) |
| 20.0.25187809928912253401368511601.1 | x20 - x19 + 10x18 - 9x17 + 65x16 - 54x15 + 235x14 - 148x13 + 574x12 - 298x11 + 830x10 - 201x9 + 704x8 - 124x7 + 362x6 + 15x5 + 91x4 + 10x3 + 17x2 + 3x + 1 | \( 3^{10}\cdot 37^{2}\cdot 47^{2}\cdot 239^{2}\cdot 1571417^{2} \) | 20T1021 | $[12]$ (GRH) |
| 20.0.26496929674942114598525390625.1 | x20 - x19 + 14x18 - 3x17 + 131x16 - 23x15 + 547x14 + 141x13 + 1496x12 + 223x11 + 1987x10 + 109x9 + 1892x8 - 114x7 + 860x6 - 175x5 + 293x4 - 40x3 + 27x2 + 3x + 1 | \( 3^{10}\cdot 5^{10}\cdot 11^{16} \) | $C_2\times C_{10}$ (as 20T3) | $[11]$ |
| 20.0.34371041692793369293212890625.1 | x20 + 10x18 + 65x16 - x15 + 250x14 - 15x13 + 700x12 - 75x11 + 1252x10 - 250x9 + 1620x8 - 375x7 + 1200x6 - 374x5 + 600x4 - 115x3 + 50x2 + 5x + 1 | \( 3^{10}\cdot 5^{34} \) | $C_2\times C_{10}$ (as 20T3) | $[11]$ |
| 20.0.49008711322611047193837890625.1 | x20 - 4x19 + 19x18 - 32x17 + 95x16 - 91x15 + 320x14 - 163x13 + 676x12 - 43x11 + 1048x10 + 129x9 + 927x8 + 299x7 + 576x6 + 152x5 + 130x4 + 34x3 + 21x2 + 4x + 1 | \( 3^{10}\cdot 5^{10}\cdot 419^{2}\cdot 695771^{2} \) | 20T656 | $[15]$ (GRH) |
| 20.0.55338861907337413914931640625.1 | x20 - x19 + 11x18 - 6x17 + 74x16 - 35x15 + 289x14 - 114x13 + 804x12 - 320x11 + 1455x10 - 554x9 + 1882x8 - 802x7 + 1473x6 - 659x5 + 810x4 - 316x3 + 149x2 - 13x + 1 | \( 3^{10}\cdot 5^{10}\cdot 11^{2}\cdot 28162171^{2} \) | 20T656 | $[2, 6]$ (GRH) |
| 20.0.119897383984074477569580078125.1 | x20 - 6x19 + 30x18 - 100x17 + 285x16 - 662x15 + 1266x14 - 1564x13 + 1560x12 - 2105x11 + 4112x10 - 6402x9 + 7316x8 - 5906x7 + 3515x6 - 1610x5 + 643x4 - 206x3 + 52x2 - 9x + 1 | \( 5^{15}\cdot 211^{8} \) | $C_5\times C_5:C_4$ (as 20T25) | $[11]$ |
| 20.0.289632434699042000000000000000.1 | x20 - 4x19 + 10x18 - 17x17 + 51x16 - 52x15 + 96x14 - 96x13 + 410x12 - 306x11 + 986x10 + 110x9 + 963x8 + 218x7 + 462x6 + 59x5 + 126x4 - 72x3 + 32x2 - 7x + 1 | \( 2^{16}\cdot 5^{15}\cdot 3469^{4} \) | $D_5^2:C_4$ (as 20T93) | $[4, 4]$ (GRH) |
| 20.0.344255425354822086003595935744.1 | x20 + 21x18 + 188x16 + 934x14 + 2806x12 + 5202x10 + 5809x8 + 3629x6 + 1090x4 + 120x2 + 1 | \( 2^{20}\cdot 3^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[22]$ (GRH) |
| 20.0.344255425354822086003595935744.2 | x20 + 11x18 + 77x16 + 330x14 + 1034x12 + 2189x10 + 3388x8 + 3267x6 + 2178x4 + 605x2 + 121 | \( 2^{20}\cdot 3^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[22]$ (GRH) |
| 20.0.344255425354822086003595935744.3 | x20 + 3x18 + 9x16 + 27x14 + 81x12 + 243x10 + 729x8 + 2187x6 + 6561x4 + 19683x2 + 59049 | \( 2^{20}\cdot 3^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[22]$ (GRH) |
| 20.0.379627024808728330240000000000.1 | x20 + 23x18 + 211x16 + 1006x14 + 2709x12 + 4193x10 + 3661x8 + 1730x6 + 399x4 + 35x2 + 1 | \( 2^{28}\cdot 5^{10}\cdot 3469^{4} \) | $C_2\times D_5\wr C_2$ (as 20T100) | $[11]$ (GRH) |
| 20.0.434388454223632138240000000000.1 | x20 - 10x19 + 37x18 - 48x17 + 20x16 - 364x15 + 1682x14 - 2752x13 + 2485x12 - 6746x11 + 22037x10 - 39472x9 + 50334x8 - 61168x7 + 82996x6 - 101248x5 + 96184x4 - 66080x3 + 30304x2 - 8192x + 1024 | \( 2^{30}\cdot 5^{10}\cdot 23^{10} \) | $D_{10}$ (as 20T4) | $[2, 6]$ (GRH) |
| 20.0.470525233802978928640000000000.1 | x20 + 27x18 + 277x16 + 1386x14 + 3694x12 + 5493x10 + 4588x8 + 2079x6 + 470x4 + 45x2 + 1 | \( 2^{20}\cdot 5^{10}\cdot 11^{16} \) | $C_2\times C_{10}$ (as 20T3) | $[31]$ (GRH) |
| 20.0.610351562500000000000000000000.1 | x20 + 20x18 + 170x16 + 800x14 + 2275x12 + 4003x10 + 4280x8 + 2605x6 + 775x4 + 75x2 + 1 | \( 2^{20}\cdot 5^{34} \) | $C_2\times C_{10}$ (as 20T3) | $[55]$ (GRH) |
| 20.0.626181899727703906518837890625.1 | x20 - 2x19 + 13x18 - 12x17 + 84x16 - 62x15 + 334x14 - 131x13 + 835x12 - 261x11 + 1424x10 - 259x9 + 1546x8 - 391x7 + 1026x6 - 217x5 + 393x4 - 148x3 + 53x2 - 8x + 1 | \( 3^{10}\cdot 5^{10}\cdot 19^{4}\cdot 1699^{4} \) | $C_2\times D_5\wr C_2$ (as 20T100) | $[31]$ (GRH) |
| 20.0.762378983303206514165048828125.1 | x20 - 3x19 + 11x18 - 9x17 + 29x16 + 26x15 + 169x14 - 45x13 + 1028x12 + 812x11 + 2595x10 + 2965x9 + 6133x8 + 7447x7 + 9309x6 + 8419x5 + 6763x4 + 4568x3 + 2598x2 + 900x + 139 | \( 5^{10}\cdot 61^{7}\cdot 397^{4} \) | 20T174 | $[2, 8]$ (GRH) |
| 20.0.766481815643182771348259698369.1 | x20 - x19 + 4x18 - 7x17 + 19x16 - 40x15 + 97x14 - 217x13 + 508x12 - 1159x11 + 2683x10 + 3477x9 + 4572x8 + 5859x7 + 7857x6 + 9720x5 + 13851x4 + 15309x3 + 26244x2 + 19683x + 59049 | \( 11^{18}\cdot 13^{10} \) | $C_2\times C_{10}$ (as 20T3) | $[25]$ (GRH) |
| 20.0.822190157101803765760000000000.1 | x20 - 4x18 - 12x16 + 344x14 - 1760x12 + 2528x10 + 19328x8 - 15232x6 - 185856x4 + 1062400x2 + 615424 | \( 2^{30}\cdot 5^{10}\cdot 601^{5} \) | $C_2\times D_5\wr C_2$ (as 20T92) | $[20]$ (GRH) |
| 20.0.944752023481393470132431640625.1 | x20 + 7x18 + 62x16 + 176x14 + 839x12 + 403x10 + 4183x8 - 7656x6 + 17915x4 - 38130x2 + 39601 | \( 5^{10}\cdot 11^{16}\cdot 1451^{2} \) | $C_2^2\times C_2^4:C_5$ (as 20T86) | $[30]$ (GRH) |
| 20.0.1124462134942353310118447265625.1 | x20 - 4x19 + 20x18 - 60x17 + 170x16 - 371x15 + 715x14 - 1078x13 + 1399x12 - 1034x11 + 1299x10 + 2068x9 + 5596x8 + 8624x7 + 11440x6 + 11872x5 + 10880x4 + 7680x3 + 5120x2 + 2048x + 1024 | \( 5^{10}\cdot 11^{16}\cdot 1583^{2} \) | $C_2^2\times C_2^4:C_5$ (as 20T86) | $[33]$ (GRH) |
| 20.0.1134723530638764277760000000000.1 | x20 + 12x18 + 12x16 - 720x14 - 4464x12 + 1696x10 + 100224x8 + 417024x6 + 903168x4 + 1142784x2 + 656384 | \( 2^{30}\cdot 5^{10}\cdot 641^{5} \) | $C_2\times D_5\wr C_2$ (as 20T92) | $[16]$ (GRH) |
| 20.0.1473037853855871696037385076736.1 | x20 + 19x18 + 147x16 + 608x14 + 1472x12 + 2137x10 + 1828x8 + 872x6 + 212x4 + 24x2 + 1 | \( 2^{20}\cdot 43^{2}\cdot 47^{2}\cdot 61^{4}\cdot 397^{4} \) | 20T799 | $[48]$ (GRH) |
| 20.0.1631471870594231356489225732096.1 | x20 + 15x18 + 71x16 + 64x14 - 206x12 + 232x10 + 10289x8 - 10258x6 + 103684x4 - 97336x2 + 279841 | \( 2^{20}\cdot 11^{18}\cdot 23^{4} \) | $C_2\times C_2^4:C_5$ (as 20T44) | $[2, 14]$ (GRH) |
| 20.0.1631471870594231356489225732096.2 | x20 + 16x18 + 256x16 + 2226x14 + 8094x12 + 6942x10 - 15153x8 - 23713x6 + 205781x4 - 292008x2 + 279841 | \( 2^{20}\cdot 11^{18}\cdot 23^{4} \) | $C_2\times C_2^4:C_5$ (as 20T44) | $[2, 16]$ (GRH) |
| 20.0.1950870747766649155582852857856.1 | x20 + 12x18 + 67x16 + 182x14 + 295x12 + 110x10 + 12x8 - 334x6 + 493x4 - 320x2 + 81 | \( 2^{40}\cdot 36497^{4} \) | 20T368 | $[12]$ (GRH) |
| 20.0.2265542600600196424321962890625.1 | x20 - 2x19 + 16x18 - 28x17 + 171x16 - 274x15 + 844x14 - 790x13 + 2040x12 - 1794x11 + 3161x10 - 1998x9 + 2627x8 - 1573x7 + 1420x6 - 526x5 + 245x4 - 47x3 + 20x2 - 3x + 1 | \( 3^{10}\cdot 5^{10}\cdot 211^{8} \) | $C_{10}\times D_5$ (as 20T24) | $[5, 5]$ (GRH) |
| 20.0.2277742396626621674993797300224.1 | x20 + 13x18 + 58x16 + 89x14 - 82x12 - 396x10 - 129x8 + 653x6 + 599x4 + 57x2 + 1 | \( 2^{20}\cdot 3^{2}\cdot 19^{2}\cdot 401^{8} \) | 20T412 | $[18]$ (GRH) |
| 20.0.2277742396626621674993797300224.3 | x20 + 17x18 + 110x16 + 378x14 + 786x12 + 1030x10 + 866x8 + 469x6 + 154x4 + 25x2 + 1 | \( 2^{20}\cdot 3^{2}\cdot 19^{2}\cdot 401^{8} \) | 20T412 | $[2, 6]$ (GRH) |
| 20.0.2433062929616749991460283088896.1 | x20 - x16 - 50x14 + 235x12 - 264x10 + 607x8 - 764x6 + 282x4 + 456x2 + 121 | \( 2^{40}\cdot 38569^{4} \) | 20T368 | $[12]$ (GRH) |
| 20.0.2899386483136048131727057286409.1 | x20 - 2x19 + 17x18 - 4x17 + 155x16 - 50x15 + 621x14 - 17x13 + 1572x12 + 87x11 + 2525x10 + 811x9 + 2589x8 + 1042x7 + 1857x6 + 907x5 + 667x4 + 142x3 + 44x2 - 4x + 1 | \( 3^{10}\cdot 271^{2}\cdot 401^{8} \) | 20T141 | $[2, 12]$ (GRH) |
| 20.0.2913368227796180298080018497536.1 | x20 - 2x19 + 7x18 + 26x17 - 70x16 + 158x15 + 469x14 - 1982x13 + 4033x12 - 1612x11 - 6028x10 + 14984x9 - 10492x8 - 8320x7 + 33296x6 - 47040x5 + 44688x4 - 30336x3 + 15232x2 - 5120x + 1024 | \( 2^{30}\cdot 3^{10}\cdot 11^{16} \) | $D_{10}$ (as 20T4) | $[5, 5]$ (GRH) |
| 20.0.2913368227796180298080018497536.4 | x20 + 18x18 + 212x16 + 1456x14 + 7264x12 + 22752x10 + 50944x8 + 60032x6 + 48640x4 + 7680x2 + 1024 | \( 2^{30}\cdot 3^{10}\cdot 11^{16} \) | $C_2\times C_{10}$ (as 20T3) | $[5, 5]$ (GRH) |
| 20.0.3045133133202651972569845989376.1 | x20 + 19x18 + 148x16 + 617x14 + 1507x12 + 2218x10 + 1946x8 + 970x6 + 249x4 + 27x2 + 1 | \( 2^{36}\cdot 83^{4}\cdot 983^{4} \) | 20T673 | $[2, 26]$ (GRH) |
| 20.0.3206128490667995866421572265625.1 | x20 - x19 + 19x18 - 15x17 + 148x16 - 88x15 + 618x14 - 266x13 + 1534x12 - 470x11 + 2342x10 - 263x9 + 1906x8 + 1335x7 + 479x6 + 2937x5 - 134x4 + 3709x3 - 1963x2 - 1928x + 9901 | \( 3^{10}\cdot 5^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[44]$ (GRH) |
| 20.0.3206128490667995866421572265625.3 | x20 - x19 - 3x18 + 7x17 + 5x16 - 33x15 + 13x14 + 119x13 - 171x12 - 305x11 + 989x10 - 1220x9 - 2736x8 + 7616x7 + 3328x6 - 33792x5 + 20480x4 + 114688x3 - 196608x2 - 262144x + 1048576 | \( 3^{10}\cdot 5^{10}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[2, 22]$ (GRH) |
| 20.0.3642745164401140602041259765625.1 | x20 + 9x18 - 11x17 + 80x16 - 132x15 + 370x14 - 771x13 + 1774x12 - 3647x11 + 6326x10 - 11208x9 + 16824x8 - 22586x7 + 31893x6 - 30556x5 + 31624x4 - 27418x3 + 13365x2 - 7827x + 5659 | \( 5^{12}\cdot 419^{4}\cdot 695771^{2} \) | 20T1040 | $[2, 20]$ (GRH) |
| 20.0.3839372453113070701618634162176.2 | x20 - 4x19 - 10x18 + 68x17 + 39x16 - 672x15 + 752x14 + 2396x13 - 8045x12 + 6116x11 + 22752x10 - 60492x9 + 8422x8 + 126032x7 - 108124x6 - 108680x5 + 262425x4 - 242232x3 + 161216x2 - 82360x + 21025 | \( 2^{30}\cdot 11^{10}\cdot 13^{10} \) | $D_{10}$ (as 20T4) | $[12]$ (GRH) |
| 20.0.3922025930637479853172889160481.1 | x20 - 10x19 + 45x18 - 120x17 + 236x16 - 460x15 + 962x14 - 1744x13 + 2560x12 - 3452x11 + 4808x10 - 6402x9 + 7229x8 - 6630x7 + 4107x6 - 492x5 - 708x4 - 394x3 + 1146x2 - 682x + 961 | \( 191^{2}\cdot 401^{10} \) | $C_2\times C_2^4:D_5$ (as 20T81) | $[17]$ (GRH) |
| 20.0.4124166770359015413760000000000.1 | x20 + 10x18 - 31x16 - 390x14 + 476x12 + 4449x10 - 4671x8 - 4287x6 + 17411x4 + 15564x2 + 3319 | \( 2^{20}\cdot 5^{10}\cdot 3319^{5} \) | 20T168 | $[28]$ (GRH) |
| 20.0.4378748240839483381760000000000.1 | x20 + 10x18 + 29x16 + 10x14 - 44x12 + 381x10 + 4489x8 + 18337x6 + 30671x4 + 17956x2 + 3359 | \( 2^{20}\cdot 5^{10}\cdot 3359^{5} \) | 20T168 | $[20]$ (GRH) |
| 20.0.5938531341125635825289072265625.1 | x20 - 8x19 + 52x18 - 244x17 + 937x16 - 2998x15 + 8069x14 - 18569x13 + 36392x12 - 59462x11 + 78193x10 - 84235x9 + 79306x8 - 66389x7 + 51585x6 - 30332x5 + 17988x4 - 7417x3 + 3436x2 - 817x + 361 | \( 5^{10}\cdot 239^{10} \) | $D_{10}$ (as 20T4) | $[12]$ (GRH) |
| 20.0.6113193735657808322804901216256.4 | x20 + 33x16 + 352x12 + 1331x8 + 1331x4 + 121 | \( 2^{40}\cdot 11^{18} \) | $C_2\times C_{10}$ (as 20T3) | $[22]$ (GRH) |
| 20.0.6348282919278872504865709055049.1 | x20 - 6x19 + 13x18 - 6x17 - 8x16 - 78x15 + 186x14 + 366x13 - 1637x12 + 1206x11 + 3082x10 - 9678x9 + 39901x8 - 165879x7 + 443766x6 - 798225x5 + 1041604x4 - 1035804x3 + 776719x2 - 392763x + 100489 | \( 3^{10}\cdot 401^{10} \) | $D_{10}$ (as 20T4) | $[2, 2, 2, 6]$ (GRH) |
| 20.0.6839529046897455541684062388224.1 | x20 - 3x18 + 54x16 - 167x14 + 1188x12 - 3348x10 + 1282x8 + 13080x6 + 18288x4 - 7695x2 + 729 | \( 2^{20}\cdot 3^{10}\cdot 101^{10} \) | $D_{10}$ (as 20T4) | $[14]$ (GRH) |
| 20.0.7063749884567622760178373361664.1 | x20 + 23x18 + 220x16 + 1138x14 + 3470x12 + 6387x10 + 7010x8 + 4398x6 + 1448x4 + 213x2 + 11 | \( 2^{20}\cdot 11\cdot 17^{4}\cdot 157^{2}\cdot 4153^{4} \) | 20T1015 | $[54]$ (GRH) |
| 20.0.7920520435441515997440262537216.1 | x20 - 2x18 + 7x16 - 2x14 + 5x12 + 28x10 + 20x8 - 32x6 + 448x4 - 512x2 + 1024 | \( 2^{24}\cdot 31^{2}\cdot 53^{12} \) | 20T196 | $[12]$ (GRH) |
| 20.0.8594615979728083252716064453125.1 | x20 - 4x19 + 13x18 + 8x17 + 71x16 + 110x15 + 364x14 + 682x13 + 1267x12 + 2089x11 + 2423x10 + 2229x9 + 1652x8 + 1042x7 + 1314x6 + 220x5 + 1556x4 - 787x3 + 428x2 - 24x + 1 | \( 3^{4}\cdot 5^{17}\cdot 23^{4}\cdot 89^{6} \) | 20T886 | $[2, 8]$ (GRH) |
| 20.0.10473339213126553396125334765568.1 | x20 - 4x18 - 6x16 + 4x14 + 265x12 + 72x10 + 1092x8 - 64x6 + 14528x4 + 16896x2 + 51200 | \( 2^{27}\cdot 727^{8} \) | 20T525 | $[11]$ (GRH) |
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