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Label Polynomial Discriminant Galois group Class group
22.0.1163485434252431102394067.1 x22 - 2x21 + 6x20 - 12x19 + 22x18 - 40x17 + 62x16 - 97x15 + 138x14 - 177x13 + 216x12 - 233x11 + 238x10 - 226x9 + 195x8 - 164x7 + 124x6 - 85x5 + 55x4 - 29x3 + 13x2 - 5x + 1 \( -\,971^{2}\cdot 1867\cdot 25709231^{2} \) 22T53 Trivial (GRH)
22.0.3273714539904703691187619.1 x22 - x21 - 7x19 + 8x18 + 7x17 + 17x16 - 26x15 - 35x14 - 4x13 + 68x12 + 92x11 + 10x10 - 49x9 - 27x8 + 32x7 + 57x6 + 24x5 - 13x4 - 17x3 - 3x2 + 2x + 1 \( -\,61\cdot 1279\cdot 1609^{2}\cdot 4025911^{2} \) 22T53 Trivial (GRH)
22.0.4514211640352695524009371.1 x22 + 2x20 - 5x19 - 4x18 - 9x17 + 8x16 + 16x15 + 29x14 - 7x13 - 29x12 - 55x11 + 4x10 + 37x9 + 57x8 - 3x7 - 30x6 - 33x5 + 7x4 + 12x3 + 5x2 - 3x + 1 \( -\,11^{4}\cdot 181^{2}\cdot 101771\cdot 304099^{2} \) 22T53 Trivial (GRH)
22.2.41217344982318472393444237.1 x22 - 7x20 - 3x19 + 17x18 + 12x17 - 15x16 - 16x15 - x14 - x13 - 28x12 - 42x11 + 3x10 + 25x9 - 16x8 - 47x7 - 35x6 + 7x5 + 16x4 - 7x3 - 5x2 + 2x + 1 \( 1070197\cdot 6205948139^{2} \) 22T53 Trivial (GRH)
22.2.178901193768541138691065033.1 x22 - 11x21 + 65x20 - 265x19 + 825x18 - 2067x17 + 4301x16 - 7582x15 + 11469x14 - 15003x13 + 17039x12 - 16811x11 + 14374x10 - 10594x9 + 6680x8 - 3576x7 + 1630x6 - 656x5 + 261x4 - 113x3 + 48x2 - 15x + 1 \( 149\cdot 33797\cdot 64661^{2}\cdot 92179^{2} \) 22T53 Trivial (GRH)
22.2.289863980721044983135295513.1 x22 - x21 + x20 - 3x19 + 3x18 + x17 + 5x16 - 4x15 - 18x14 + 11x13 + 16x12 + 32x11 - 45x10 - 81x9 + 100x8 + 75x7 - 101x6 - 41x5 + 53x4 + 15x3 - 15x2 - 4x + 1 \( 359753\cdot 28385393161^{2} \) 22T53 Trivial (GRH)
22.6.440358787157109245022232573.1 x22 - 11x21 + 64x20 - 255x19 + 770x18 - 1857x17 + 3688x16 - 6146x15 + 8690x14 - 10480x13 + 10777x12 - 9386x11 + 6807x10 - 3960x9 + 1680x8 - 341x7 - 170x6 + 212x5 - 109x4 + 28x3 + 3x2 - 5x + 1 \( 37\cdot 163^{2}\cdot 14281\cdot 177106931^{2} \) 22T53 Trivial (GRH)
22.4.951194438369517944038992707.1 x22 - 11x21 + 66x20 - 275x19 + 879x18 - 2268x17 + 4871x16 - 8878x15 + 13903x14 - 18847x13 + 22192x12 - 22691x11 + 20056x10 - 15173x9 + 9644x8 - 4974x7 + 1932x6 - 448x5 - 27x4 + 71x3 - 24x2 + x + 1 \( -\,139\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2}\cdot 9473 \) 22T53 Trivial (GRH)
22.4.969538443288973935184255159.1 x22 - x21 + 3x20 + 3x18 + 5x17 + 7x16 + 4x15 + 12x14 - 17x13 - 35x11 - 28x10 - 29x9 - 20x8 - 6x7 - 11x6 - 26x5 - 22x4 - 11x3 - 4x2 + 9x - 1 \( -\,173\cdot 7043\cdot 28208540809^{2} \) 22T53 Trivial (GRH)
22.10.1622619348151146292612416109.1 x22 - 5x21 + 4x20 + 19x19 - 39x18 + 11x17 - 8x16 + 47x15 + 183x14 - 603x13 + 274x12 + 853x11 - 1093x10 - 146x9 + 897x8 - 256x7 - 277x6 + 109x5 + 47x4 - 10x3 - 11x2 + x + 1 \( 29101\cdot 372881^{2}\cdot 633263^{2} \) 22T53 Trivial (GRH)
22.4.1897242698910438481935564683.1 x22 - x21 + x20 + x19 + x18 + 5x17 - 11x16 + 6x15 + 19x14 - 22x13 - 4x12 + 6x11 + 13x10 + 26x9 - 75x8 - 11x7 + 101x6 - 32x5 - 59x4 + 28x3 + 15x2 - 6x - 1 \( -\,47147\cdot 200601609583^{2} \) 22T53 Trivial (GRH)
22.0.2613825179875044875466440704.1 x22 + 6x20 + 16x18 + 18x16 + 4x14 + 6x12 + 25x10 + 3x8 - 19x6 - 4x4 + 4x2 + 1 \( -\,2^{22}\cdot 971^{2}\cdot 25709231^{2} \) 22T53 Trivial (GRH)
22.6.11179894991688395891652264149.1 x22 - 11x21 + 44x20 - 55x19 - 111x18 + 372x17 - 61x16 - 838x15 + 563x14 + 1153x13 - 1030x12 - 1191x11 + 1050x10 + 987x9 - 634x8 - 630x7 + 192x6 + 264x5 - 3x4 - 53x3 - 10x2 + x - 1 \( 83\cdot 199\cdot 937\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2} \) 22T53 Trivial (GRH)
22.8.14799420881562079578038490499.1 x22 - 11x21 + 44x20 - 55x19 - 112x18 + 381x17 - 87x16 - 834x15 + 674x14 + 1020x13 - 1213x12 - 834x11 + 1220x10 + 511x9 - 776x8 - 247x7 + 323x6 + 85x5 - 89x4 - 18x3 + 16x2 + x - 1 \( -\,97\cdot 2381^{2}\cdot 2467\cdot 104446171^{2} \) 22T53 Trivial (GRH)
22.10.70442637605798451973179258449.1 x22 - 11x21 + 43x20 - 45x19 - 147x18 + 411x17 + 19x16 - 1070x15 + 605x14 + 1553x13 - 1312x12 - 1553x11 + 1432x10 + 1195x9 - 928x8 - 712x7 + 352x6 + 291x5 - 71x4 - 67x3 + 7x2 + 7x - 1 \( 71^{2}\cdot 1282529\cdot 3300850529^{2} \) 22T53 Trivial (GRH)
22.0.73443346282868916473942769664.1 x22 + 13x20 + 75x18 + 255x16 + 572x14 + 895x12 + 999x10 + 790x8 + 425x6 + 140x4 + 21x2 + 1 \( -\,2^{22}\cdot 211441^{2}\cdot 625831^{2} \) 22T53 Trivial (GRH)
22.8.104070916689387515610916716544.1 x22 - 2x20 - x18 - 2x16 + 18x12 - 24x10 - 3x8 + 36x6 - 27x4 + 4x2 + 1 \( -\,2^{22}\cdot 19457^{2}\cdot 8095783^{2} \) 22T53 Trivial (GRH)
22.0.117045760309296676701139369984.1 x22 + 2x20 - x16 - 7x14 - 14x12 - x10 + 9x8 + 15x6 + 22x4 + 10x2 + 1 \( -\,2^{22}\cdot 2089^{2}\cdot 79966751^{2} \) 22T53 Trivial (GRH)
22.4.1562900555060447098970765787136.1 x22 + 10x20 + 41x18 + 85x16 + 79x14 - 14x12 - 98x10 - 74x8 - 3x6 + 22x4 + 9x2 + 1 \( -\,2^{22}\cdot 610429790897^{2} \) 22T53 Trivial (GRH)
22.8.1562900555060447098970765787136.1 x22 - x20 - 4x18 + x16 + 5x14 + 7x12 - 7x10 - 5x8 + 7x6 - 3x4 - x2 + 1 \( -\,2^{22}\cdot 610429790897^{2} \) 22T53 Trivial (GRH)
22.4.1562900555060447098970765787136.2 x22 - 7x20 + 15x18 - 4x16 - 28x14 + 36x12 + 7x10 - 49x8 - 5x6 + 24x4 + 10x2 + 1 \( -\,2^{22}\cdot 610429790897^{2} \) 22T53 Trivial (GRH)
22.6.1815714277580347556883155703869.1 x22 - 11x21 + 64x20 - 255x19 + 769x18 - 1848x17 + 3647x16 - 6022x15 + 8418x14 - 10032x13 + 10228x12 - 8926x11 + 6647x10 - 4183x9 + 2160x8 - 829x7 + 136x6 + 111x5 - 114x4 + 47x3 - 3x2 - 5x + 1 \( 71^{2}\cdot 73^{2}\cdot 1408829\cdot 219034943^{2} \) 22T53 Trivial (GRH)
22.8.2741869623221317890608793124864.1 x22 - 2x20 - x18 + 4x16 - x14 - 5x12 - x10 + 8x8 + 3x6 - 5x4 - x2 + 1 \( -\,2^{22}\cdot 43^{2}\cdot 547^{2}\cdot 34374601^{2} \) 22T53 Trivial (GRH)
22.12.10994531599582075769676214829056.1 x22 - 10x20 + 44x18 - 112x16 + 182x14 - 199x12 + 151x10 - 67x8 - 13x6 + 36x4 - 13x2 + 1 \( -\,2^{22}\cdot 1619043113033^{2} \) 22T53 Trivial (GRH)
22.12.10994531599582075769676214829056.2 x22 - 12x20 + 64x18 - 200x16 + 406x14 - 557x12 + 507x10 - 271x8 + 51x6 + 18x4 - 9x2 + 1 \( -\,2^{22}\cdot 1619043113033^{2} \) 22T53 Trivial (GRH)
22.2.12816596924190768698410425412337.1 x22 - 11x21 + 75x20 - 365x19 + 1409x18 - 4473x17 + 12052x16 - 27974x15 + 56686x14 - 100938x13 + 158847x12 - 221312x11 + 273270x10 - 298381x9 + 287150x8 - 241819x7 + 176511x6 - 109912x5 + 57096x4 - 23845x3 + 7532x2 - 1599x + 163 \( 31\cdot 43^{2}\cdot 547^{2}\cdot 632447\cdot 34374601^{2} \) 22T53 Trivial (GRH)
22.0.13471519681654627790892423970816.1 x22 + 12x20 + 64x18 + 200x16 + 403x14 + 544x12 + 510x10 + 358x8 + 197x6 + 73x4 + 14x2 + 1 \( -\,2^{22}\cdot 1792166448977^{2} \) 22T53 Trivial (GRH)
22.6.17629227795712151522876415102277.1 x22 - 11x21 + 64x20 - 255x19 + 769x18 - 1848x17 + 3645x16 - 6006x15 + 8346x14 - 9808x13 + 9702x12 - 7954x11 + 5209x10 - 2471x9 + 537x8 + 363x7 - 501x6 + 318x5 - 120x4 + 16x3 + 13x2 - 9x + 1 \( 349^{2}\cdot 1697\cdot 1949\cdot 6615221297^{2} \) 22T53 Trivial (GRH)
22.0.155979617226877172002898926703507.1 x22 - 11x21 + 76x20 - 375x19 + 1474x18 - 4773x17 + 13158x16 - 31314x15 + 65238x14 - 119692x13 + 194559x12 - 280546x11 + 359279x10 - 407518x9 + 408092x8 - 358073x7 + 272834x6 - 177710x5 + 97035x4 - 42912x3 + 14655x2 - 3477x + 467 \( -\,23\cdot 2879\cdot 3371\cdot 56509^{2}\cdot 14792861^{2} \) 22T53 $[2]$ (GRH)
22.14.191266300800812904024665746296529.1 x22 - 11x21 + 43x20 - 45x19 - 146x18 + 402x17 + 46x16 - 1082x15 + 512x14 + 1700x13 - 1234x12 - 1826x11 + 1419x10 + 1403x9 - 797x8 - 807x7 + 55x6 + 331x5 + 160x4 - 51x3 - 59x2 - 14x - 1 \( 7\cdot 251\cdot 33893\cdot 1792166448977^{2} \) 22T53 Trivial (GRH)
22.12.237871803919090816246272099352576.1 x22 - 12x20 + 59x18 - 151x16 + 204x14 - 106x12 - 64x10 + 101x8 - 19x6 - 16x4 + 3x2 + 1 \( -\,2^{22}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2} \) 22T53 Trivial (GRH)
22.8.237871803919090816246272099352576.1 x22 - x20 - 6x18 + 5x16 + 10x14 - 8x12 + 5x8 - 10x6 - 2x4 + 4x2 + 1 \( -\,2^{22}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2} \) 22T53 Trivial (GRH)
22.16.289690752824370116310308034941759.1 x22 - 11x21 + 43x20 - 45x19 - 152x18 + 456x17 - 114x16 - 1026x15 + 1114x14 + 790x13 - 1814x12 + 120x11 + 1304x10 - 464x9 - 493x8 + 217x7 + 170x6 - 46x5 - 77x4 + 9x3 + 18x2 - 1 \( -\,809\cdot 4759\cdot 8674315276967^{2} \) 22T53 Trivial (GRH)
22.4.315595142827230969392399757869056.1 x22 + 12x20 + 58x18 + 144x16 + 193x14 + 130x12 + 21x10 - 40x8 - 45x6 - 18x4 + 1 \( -\,2^{22}\cdot 8674315276967^{2} \) 22T53 Trivial (GRH)
22.4.316932538277153190033818958954496.1 x22 + 14x20 + 84x18 + 285x16 + 607x14 + 843x12 + 745x10 + 363x8 + 45x6 - 29x4 - 6x2 + 1 \( -\,2^{22}\cdot 151^{2}\cdot 2311^{2}\cdot 24910163^{2} \) 22T53 Trivial (GRH)
22.14.1252214624578349298453638315804341.1 x22 - 11x21 + 34x20 + 45x19 - 419x18 + 294x17 + 2039x16 - 2950x15 - 5716x14 + 11278x13 + 10840x12 - 25208x11 - 15904x10 + 35866x9 + 19724x8 - 31917x7 - 19447x6 + 15438x5 + 12389x4 - 1977x3 - 3512x2 - 887x - 59 \( 113\cdot 29739173\cdot 610429790897^{2} \) 22T53 Trivial (GRH)
22.12.1288033148279983900699565800554496.1 x22 - 8x20 + 24x18 - 28x16 - 12x14 + 66x12 - 48x10 - 28x8 + 43x6 - 3x4 - 7x2 + 1 \( -\,2^{22}\cdot 17524013040643^{2} \) 22T53 Trivial (GRH)
22.16.1288033148279983900699565800554496.1 x22 - 14x20 + 84x18 - 284x16 + 596x14 - 794x12 + 632x10 - 220x8 - 53x6 + 65x4 - 15x2 + 1 \( -\,2^{22}\cdot 17524013040643^{2} \) 22T53 Trivial (GRH)
22.8.1288033148279983900699565800554496.1 x22 + 3x20 - x18 - 7x16 - 2x14 - 4x12 - 2x10 + 16x8 + 4x6 - 9x4 - x2 + 1 \( -\,2^{22}\cdot 17524013040643^{2} \) 22T53 Trivial (GRH)
22.6.2009643344565206347646133417459817.1 x22 - 11x21 + 63x20 - 245x19 + 714x18 - 1638x17 + 3034x16 - 4586x15 + 5635x14 - 5481x13 + 3863x12 - 1247x11 - 1359x10 + 2985x9 - 3236x8 + 2436x7 - 1301x6 + 435x5 - 37x4 - 42x3 + 18x2 - x - 1 \( 37\cdot 131\cdot 431\cdot 31015897276291^{2} \) 22T53 $[2]$ (GRH)
22.18.10184378952996122520694192412373661.1 x22 - 11x21 + 40x20 - 15x19 - 254x18 + 519x17 + 310x16 - 1970x15 + 1107x14 + 2977x13 - 3993x12 - 1171x11 + 5121x10 - 1997x9 - 2876x8 + 2700x7 + 340x6 - 1207x5 + 283x4 + 173x3 - 80x2 + 3x + 1 \( 3363181\cdot 55029067682009^{2} \) 22T53 Trivial (GRH)
22.12.12701184200335173359101913935642624.1 x22 - 7x20 + 11x18 + 20x16 - 54x14 - 17x12 + 80x10 + 11x8 - 43x6 - 9x4 + 5x2 + 1 \( -\,2^{22}\cdot 55029067682009^{2} \) 22T53 Trivial (GRH)
22.16.12701184200335173359101913935642624.1 x22 - 15x20 + 91x18 - 278x16 + 410x14 - 123x12 - 404x10 + 417x8 - 19x6 - 77x4 - 3x2 + 1 \( -\,2^{22}\cdot 55029067682009^{2} \) 22T53 Trivial (GRH)
22.12.12701184200335173359101913935642624.2 x22 - 4x20 - 4x18 + 31x16 - 8x14 - 81x12 + 48x10 + 88x8 - 60x6 - 35x4 + 22x2 + 1 \( -\,2^{22}\cdot 55029067682009^{2} \) 22T53 Trivial (GRH)
22.16.13844017509319141075535476685799424.1 x22 - 11x20 + 43x18 - 52x16 - 96x14 + 332x12 - 229x10 - 230x8 + 408x6 - 186x4 + 20x2 + 1 \( -\,2^{22}\cdot 233^{2}\cdot 246572816873^{2} \) 22T53 Trivial (GRH)
22.8.13844017509319141075535476685799424.1 x22 + 11x20 + 43x18 + 62x16 - 16x14 - 116x12 - 53x10 + 56x8 + 32x6 - 10x4 - 4x2 + 1 \( -\,2^{22}\cdot 233^{2}\cdot 246572816873^{2} \) 22T53 Trivial (GRH)
22.20.15891297445653813609959315666834999.1 x22 - 11x21 + 41x20 - 25x19 - 223x18 + 525x17 + 92x16 - 1654x15 + 1480x14 + 1772x13 - 3759x12 + 506x11 + 3901x10 - 2800x9 - 1867x8 + 2565x7 + 335x6 - 1066x5 - 4x4 + 202x3 + 3x2 - 14x - 1 \( -\,79\cdot 1451^{2}\cdot 18521\cdot 71823490019^{2} \) 22T53 Trivial (GRH)
22.8.17213757945874230471135911350559867.1 x22 - 11x21 + 62x20 - 235x19 + 656x18 - 1401x17 + 2307x16 - 2850x15 + 2370x14 - 664x13 - 1547x12 + 2938x11 - 2660x10 + 1125x9 + 394x8 - 967x7 + 681x6 - 193x5 - 53x4 + 68x3 - 22x2 + x + 1 \( -\,137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2}\cdot 1849643 \) 22T53 Trivial (GRH)
22.4.33833812608216375123231853716176896.1 x22 + 16x20 + 105x18 + 363x16 + 700x14 + 709x12 + 248x10 - 146x8 - 135x6 - 20x4 + 5x2 + 1 \( -\,2^{22}\cdot 2053^{2}\cdot 43747835269^{2} \) 22T53 Trivial (GRH)
22.4.39034415726392643532837005585022976.1 x22 + 15x20 + 91x18 + 279x16 + 417x14 + 130x12 - 453x10 - 544x8 - 66x6 + 185x4 + 75x2 + 1 \( -\,2^{22}\cdot 137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2} \) 22T53 Trivial (GRH)

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