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Label Polynomial Discriminant Galois group Class group
22.0.178400853291024459894627.1 x22 + 2x20 + 5x18 - x17 + 6x16 - 3x15 + 9x14 - x13 + 7x12 - 3x11 + 13x10 + 5x8 + 3x7 + 10x6 + x4 + 4x2 + 2x + 1 \( -\,3^{11}\cdot 1003532779^{2} \) 22T47 Trivial (GRH)
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)
22.0.2817611963463158891460983.1 x22 - 4x21 + 6x20 - 8x19 + 15x18 - 9x17 - 28x16 + 46x15 - 14x14 + 23x13 + 13x12 - 297x11 + 488x10 - 240x9 + 28x8 - 134x7 + 194x6 - 130x5 + 72x4 - 28x3 + 8x2 - 2x + 1 \( -\,167^{11} \) 22T2 Trivial
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)
22.0.6250054957079127310759347.1 x22 - x20 - 4x19 + 3x18 + 3x17 + 6x16 - 9x15 + x14 - 3x13 + 9x12 - 10x11 + x10 - 2x9 + 8x8 - 5x7 - x5 + 4x4 - 2x3 + x2 + 1 \( -\,3^{11}\cdot 12917^{2}\cdot 459847^{2} \) 22T47 Trivial (GRH)
22.0.6293360649840402636051867.1 x22 - x21 - x19 + 3x18 - 3x17 - x16 + 5x14 - 3x13 - 2x12 + x11 + 6x10 - 4x9 - 2x8 - x7 + 5x6 - 2x5 - x4 - 2x3 + x2 + x + 1 \( -\,3^{11}\cdot 64661^{2}\cdot 92179^{2} \) 22T47 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)
22.0.64196743029301100734358828.1 x22 - x21 + 3x20 - 7x19 + 11x18 - 18x17 + 29x16 - 40x15 + 53x14 - 67x13 + 79x12 - 87x11 + 92x10 - 90x9 + 83x8 - 73x7 + 59x6 - 43x5 + 30x4 - 18x3 + 9x2 - 4x + 1 \( -\,2^{2}\cdot 2029\cdot 7909899338257898069783 \) 22T59 Trivial (GRH)
22.0.75348325135501798832991875.1 x22 - 4x21 + 10x20 - 22x19 + 47x18 - 79x17 + 124x16 - 169x15 + 213x14 - 229x13 + 259x12 - 192x11 + 188x10 - 90x9 + 134x8 - 14x7 + 62x6 - 19x5 + 22x4 - 12x3 + 3x2 - x + 1 \( -\,5^{4}\cdot 7^{6}\cdot 83^{5}\cdot 127^{4} \) 22T52 Trivial (GRH)
22.0.103946711888571010237690363.1 x22 - 5x21 + 15x20 - 35x19 + 68x18 - 114x17 + 170x16 - 230x15 + 285x14 - 325x13 + 343x12 - 335x11 + 306x10 - 258x9 + 202x8 - 146x7 + 97x6 - 59x5 + 32x4 - 16x3 + 7x2 - 2x + 1 \( -\,79\cdot 22109\cdot 59513372976908430233 \) 22T59 Trivial (GRH)
22.0.110395262036162513388217347.1 x22 - 4x19 + 4x16 - 4x15 + x14 - 6x13 + 7x12 - 3x11 + 12x10 + 2x9 + 18x8 + 4x7 + 13x6 + 5x5 + 6x4 + x3 + 4x2 - x + 1 \( -\,3^{11}\cdot 971^{2}\cdot 25709231^{2} \) 22T47 Trivial (GRH)
22.2.147982356498821950109384704.1 x22 - 2x20 + 6x18 - 14x16 + 22x14 - 31x12 + 38x10 - 34x8 + 27x6 - 17x4 + 6x2 - 1 \( 2^{22}\cdot 12917^{2}\cdot 459847^{2} \) 22T51 Trivial (GRH)
22.2.147982356498821950109384704.2 x22 + x18 - 2x16 - 2x14 - x12 + 3x8 + x6 + x4 - 1 \( 2^{22}\cdot 12917^{2}\cdot 459847^{2} \) 22T51 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)
22.0.492568978448025181133471744.1 x22 + 2x20 - 5x18 - 22x16 + 29x14 + 153x12 + 72x10 - 195x8 - 158x6 + 66x4 + 77x2 + 11 \( -\,2^{18}\cdot 11^{5}\cdot 19^{4}\cdot 547^{4} \) 22T52 Trivial (GRH)
22.0.577860666762298833296687104.1 x22 - 2x20 - 2x19 + 5x18 + 6x17 - 5x16 - 12x15 + 2x14 + 18x13 + 4x12 - 18x11 - 11x10 + 14x9 + 14x8 - 8x7 - 11x6 + 2x5 + 8x4 - 4x2 + 1 \( -\,2^{30}\cdot 73^{2}\cdot 577\cdot 53149\cdot 3293113 \) 22T57 Trivial (GRH)
22.0.578978183833808423828407471.1 x22 - 11x21 + 67x20 - 285x19 + 929x18 - 2433x17 + 5271x16 - 9630x15 + 15091x14 - 20633x13 + 25057x12 - 27453x11 + 27302x10 - 24426x9 + 19254x8 - 13050x7 + 7570x6 - 3890x5 + 1921x4 - 927x3 + 362x2 - 87x + 9 \( -\,271^{11} \) 22T2 Trivial (GRH)
22.2.635524829577904360423933313.1 x22 - x21 + 5x20 - 8x19 + 16x18 - 27x17 + 41x16 - 61x15 + 80x14 - 104x13 + 121x12 - 138x11 + 143x10 - 142x9 + 131x8 - 112x7 + 89x6 - 64x5 + 43x4 - 24x3 + 12x2 - 4x + 1 \( 60821\cdot 1487459\cdot 7024799976319967 \) 22T59 Trivial (GRH)
22.2.716463968651672990739595264.1 x22 + 4x20 + x18 - 20x16 - 7x14 + 93x12 + 46x10 - 121x8 - 80x6 - 34x4 - 9x2 - 1 \( 2^{22}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4} \) 22T49 Trivial (GRH)
22.2.890830078698256823295734989.1 x22 - 2x21 + 6x20 - 10x19 + 17x18 - 21x17 + 22x16 - 15x15 - 5x14 + 38x13 - 83x12 + 135x11 - 185x10 + 221x9 - 234x8 + 222x7 - 187x6 + 138x5 - 88x4 + 47x3 - 20x2 + 6x - 1 \( 34092855421\cdot 26129523845912209 \) 22T59 Trivial (GRH)
22.4.931263224878297608080470016.1 x22 - 4x21 + 5x20 + 4x19 - 26x18 + 31x17 + 15x16 - 79x15 + 76x14 + 60x13 - 153x12 + 84x11 + 83x10 - 192x9 + 24x8 + 58x7 - 150x6 + 30x5 + 19x4 - 23x3 + 6x2 + 29x + 1 \( -\,2^{12}\cdot 11^{7}\cdot 19^{4}\cdot 547^{4} \) 22T52 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)
22.0.1441291887151686135870128128.1 x22 - 2x20 - 2x19 + 5x18 + 6x17 - 5x16 - 12x15 + 2x14 + 18x13 + 4x12 - 18x11 - 11x10 + 14x9 + 15x8 - 8x7 - 12x6 + 2x5 + 8x4 - 4x2 + 1 \( -\,2^{22}\cdot 10177\cdot 33765428299628041 \) 22T57 Trivial (GRH)
22.6.1447402975463751668017578125.1 x22 - 2x21 - x20 + 18x19 - 17x18 - 44x17 + 110x16 - 3x15 - 254x14 + 59x13 + 240x12 - 102x11 - 552x10 - 230x9 + 307x8 + 320x7 - 3x6 - 154x5 - 62x4 + 18x3 + 19x2 + 2x - 1 \( 5^{11}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4} \) 22T46 Trivial (GRH)
22.4.1533107758369291702785569375.1 x22 - 2x21 + 7x20 - 20x19 + 38x18 - 74x17 + 107x16 - 167x15 + 185x14 - 284x13 + 308x12 - 417x11 + 466x10 - 462x9 + 446x8 - 292x7 + 170x6 - 55x5 - 7x4 + 11x3 - 8x2 + x + 1 \( -\,5^{4}\cdot 7^{4}\cdot 83^{5}\cdot 127^{4}\cdot 997 \) 22T52 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)
22.2.1722741365651855595751953125.1 x22 + 3x20 - 8x19 - 13x18 - 13x17 - 10x16 + 79x15 + 45x14 + 111x13 + 59x12 - 172x11 + 31x10 - 94x9 - 96x8 + 55x7 - 26x6 + x5 + 20x4 - 4x3 + 3x2 - 1 \( 5^{11}\cdot 12917^{2}\cdot 459847^{2} \) 22T47 Trivial (GRH)
22.2.1734677982017693835986328125.1 x22 - x21 + 2x20 + x19 - 13x18 + 3x17 - 35x16 - 18x15 + 37x14 + 27x13 + 152x12 + 277x11 + 160x10 + 72x9 - 42x8 - 69x7 - 31x6 - 22x5 + 3x4 + 4x3 + x2 + x - 1 \( 5^{11}\cdot 64661^{2}\cdot 92179^{2} \) 22T47 Trivial (GRH)
22.2.1767712543554828434373148672.1 x22 - 5x21 + 17x20 - 40x19 + 70x18 - 93x17 + 99x16 - 86x15 + 53x14 + 37x13 - 283x12 + 778x11 - 1493x10 + 2198x9 - 2575x8 + 2425x7 - 1840x6 + 1108x5 - 512x4 + 173x3 - 33x2 + x + 1 \( 2^{16}\cdot 37^{5}\cdot 4441^{4} \) 22T52 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)
22.6.2613825179875044875466440704.1 x22 - 6x20 + 16x18 - 18x16 + 4x14 - 6x12 + 25x10 - 3x8 - 19x6 + 4x4 + 4x2 - 1 \( 2^{22}\cdot 971^{2}\cdot 25709231^{2} \) 22T51 Trivial (GRH)
22.2.2865855874606691962958381056.1 x22 - 5x20 + 9x18 - 6x16 - 12x14 + 37x12 - 45x10 + 75x8 - 54x6 - 17x4 + 44x2 - 16 \( 2^{24}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4} \) 22T49 Trivial (GRH)
22.0.2988811416117414420033765003.1 x22 - x21 - 4x20 + 3x19 + 11x18 - 6x17 - 18x16 + 2x15 + 26x14 - 8x13 - 18x12 + 23x11 + 12x10 - 27x9 - 30x8 + 23x7 + 19x6 + 3x5 + 5x4 - 26x3 + 8x2 + 2x + 1 \( -\,3^{11}\cdot 167^{10} \) 22T3 Trivial (GRH)
22.2.3029890053010200585803137024.1 x22 + 3x20 - 11x16 - 24x14 - 24x12 + x10 + 11x8 - 9x6 - 5x4 + 5x2 - 1 \( 2^{22}\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2} \) 22T51 Trivial (GRH)
22.6.3029890053010200585803137024.1 x22 - x18 - x16 - 2x14 + x10 + 2x8 + 2x6 - 1 \( 2^{22}\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2} \) 22T51 Trivial (GRH)
22.0.3101889720909924494411835627.1 x22 - 2x21 + 4x20 - 2x18 + 9x17 - 4x16 + 6x15 + 4x14 - 2x13 + 10x12 + 7x10 + 4x9 + 2x8 + 11x7 + x6 + 3x5 + 4x4 + 2x3 + 3x2 - x + 1 \( -\,3^{11}\cdot 211441^{2}\cdot 625831^{2} \) 22T47 Trivial (GRH)
22.2.3115164990344181117349789696.1 x22 + 2x16 - x14 - x12 + x10 + x8 - 2x6 - x4 + 2x2 - 1 \( 2^{22}\cdot 1559^{2}\cdot 17480927^{2} \) 22T51 Trivial (GRH)
22.0.4395449323362095410329595467.1 x22 - x21 + 2x20 + x19 + 2x18 - x17 + 4x15 - 6x14 - 6x13 - 3x12 - x11 - 2x10 - 8x9 + 8x8 + 5x7 + 7x6 + 8x5 + 8x4 + 6x3 + 4x2 + 2x + 1 \( -\,3^{11}\cdot 19457^{2}\cdot 8095783^{2} \) 22T47 Trivial (GRH)
22.6.4525438563861162255210415625.1 x22 - 3x21 - 5x20 + 20x19 + 6x18 - 46x17 - 22x16 + 88x15 + 102x14 - 250x13 - 116x12 + 460x11 - 50x10 - 559x9 + 321x8 + 395x7 - 287x6 - 315x5 + 200x4 + 136x3 + 14x2 - 70x + 5 \( 5^{5}\cdot 7^{6}\cdot 83^{4}\cdot 127^{4}\cdot 997 \) 22T52 Trivial (GRH)
22.2.10787252710010591209601111089.1 x22 - x21 + x20 - 11x19 - 5x18 + 22x17 + 22x16 + 62x15 - 83x14 - 148x13 + 44x12 + 72x11 + 52x10 + 25x9 + 50x8 - 75x7 - 65x6 + 60x5 - 17x3 + 17x2 - 7x + 1 \( 167^{10}\cdot 639361 \) 22T32 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)
22.0.13109994191499930367061460371.1 x22 + 44x18 - 22x17 + 55x16 + 121x15 + 187x14 + 11x13 + 594x12 + 328x11 + 836x10 + 770x9 + 814x8 + 528x7 + 374x6 + 143x5 + 11x4 - 33x3 - 11x2 + 1 \( -\,11^{27} \) 22T4 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)
22.0.15257581934366008831157764375.1 x22 - 4x21 + 18x20 - 48x19 + 125x18 - 249x17 + 478x16 - 766x15 + 1216x14 - 1618x13 + 2242x12 - 2454x11 + 2995x10 - 2616x9 + 2692x8 - 1937x7 + 1684x6 - 1102x5 + 757x4 - 253x3 + 163x2 + 2x + 1 \( -\,5^{4}\cdot 7^{11}\cdot 83^{4}\cdot 127^{4} \) 22T46 Trivial (GRH)
22.6.18415764278243178646713405625.1 x22 - 7x21 + 16x20 - 3x19 - 51x18 + 101x17 - 62x16 - 50x15 + 49x14 + 124x13 - 271x12 + 166x11 + 113x10 - 102x9 - 51x8 - 34x7 + 128x6 - 78x5 - 37x4 + 36x3 + 14x2 - 8x + 1 \( 5^{4}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4}\cdot 997^{2} \) 22T49 Trivial (GRH)

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