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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 \( -\,167^{11} \) $D_{11}$ (as 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)
22.0.64196743029301100734358828.1 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)
22.0.492568978448025181133471744.1 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 \( -\,271^{11} \) $D_{11}$ (as 22T2) 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)
22.0.2613825179875044875466440704.1 x22 + 6x20 + 16x18 + 18x16 + 4x14 + 6x12 + 25x10 + 3x8 - 19x6 - 4x4 + 4x2 + 1 \( -\,2^{22}\cdot 971^{2}\cdot 25709231^{2} \) 22T53 Trivial (GRH)
22.0.2988811416117414420033765003.1 x22 - x21 - 4x20 + 3x19 + 11x18 - 6x17 - 18x16 + 2x15 + 26x14 - 8x13 - 18x12 + 23x11 + 12x10 - 27x9 - 30x8 + 23x7 + 19x6 + 3x5 + 5x4 - 26x3 + 8x2 + 2x + 1 \( -\,3^{11}\cdot 167^{10} \) $D_{22}$ (as 22T3) 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)
22.0.4395449323362095410329595467.1 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)
22.0.13109994191499930367061460371.1 x22 + 44x18 - 22x17 + 55x16 + 121x15 + 187x14 + 11x13 + 594x12 + 328x11 + 836x10 + 770x9 + 814x8 + 528x7 + 374x6 + 143x5 + 11x4 - 33x3 - 11x2 + 1 \( -\,11^{27} \) $F_{11}$ (as 22T4) 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)
22.0.45853693993707071407334096896.1 x22 + 2x20 + 3x18 - 2x16 - 7x14 - 5x12 + 4x10 + 11x8 - 2x6 - 6x4 + x2 + 1 \( -\,2^{28}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4} \) 22T46 Trivial (GRH)
22.0.58158698878603618687895783643.1 x22 - 3x11 + 3 \( -\,3^{21}\cdot 11^{18} \) $C_2\times F_{11}$ (as 22T6) Trivial (GRH)
22.0.66009317547629600105613290523.1 x22 - x21 + 5x20 + 2x19 + 12x18 + 13x17 + 14x16 + 63x15 - 7x14 + 68x13 + 31x12 + 19x11 + 40x10 - 71x9 + 84x8 - 79x7 + 41x6 - 38x5 + 21x4 - 11x3 + 4x2 - x + 1 \( -\,3^{11}\cdot 610429790897^{2} \) 22T47 Trivial (GRH)
22.0.70765994783241803539463274496.1 x22 - 9x20 + 37x18 - 94x16 + 166x14 - 214x12 + 207x10 - 149x8 + 81x6 - 34x4 + 12x2 + 1 \( -\,2^{22}\cdot 167^{10} \) $D_{22}$ (as 22T3) Trivial (GRH)
22.0.70765994783241803539463274496.2 x22 + 3x20 + 4x18 + 4x16 + 11x14 + 10x12 + 4x10 + 12x8 + 7x6 + 6x4 + 4x2 + 1 \( -\,2^{22}\cdot 167^{10} \) 22T32 Trivial (GRH)
22.0.70765994783241803539463274496.3 x22 + x20 - 7x18 - 6x16 + 23x14 + x12 - 24x10 + 21x8 - 17x6 + 9x4 - 2x2 + 1 \( -\,2^{22}\cdot 167^{10} \) 22T32 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)
22.0.115803236519047451106947869227.1 x22 - 2x21 + 5x20 - 6x19 + 10x18 - 13x17 + 3x16 - 4x15 - 15x14 + 9x13 - 23x12 + 35x11 + 5x10 + 25x9 + 40x8 + 18x7 + 38x6 + 20x4 - x3 + 6x2 - x + 1 \( -\,3^{11}\cdot 43^{2}\cdot 547^{2}\cdot 34374601^{2} \) 22T47 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)
22.0.213248562554879935188951206691.1 x22 - 4x21 + 7x20 - 12x19 + 24x18 - 33x17 + 48x16 - 51x15 + 12x14 - 2x13 + 44x12 + 193x11 - 198x10 - 426x9 + 168x8 + 372x7 + 15x6 - 99x5 - 36x4 - 36x3 - 9x2 + 18x + 9 \( -\,3^{20}\cdot 11^{19} \) $F_{11}$ (as 22T4) Trivial (GRH)
22.0.335585290345833574875265599163.1 x22 - x + 1 \( -\,3697\cdot 90772326303985278570534379 \) 22T59 Trivial (GRH)
22.0.8744435969289427463345029296875.1 x22 - 11x21 + 55x20 - 154x19 + 220x18 + 44x17 - 913x16 + 1991x15 - 1958x14 - 275x13 + 3795x12 - 5801x11 + 4323x10 - 517x9 - 2475x8 + 2772x7 - 1188x6 - 330x5 + 803x4 - 550x3 + 209x2 - 44x + 4 \( -\,5^{10}\cdot 11^{23} \) $C_2\times F_{11}$ (as 22T6) Trivial (GRH)
22.0.11817921128801381191090366840832.1 x22 + 9x20 + 37x18 + 74x16 + 22x14 - 217x12 - 442x10 - 261x8 + 291x6 + 663x4 + 501x2 + 167 \( -\,2^{22}\cdot 167^{11} \) 22T29 Trivial (GRH)
22.0.11817921128801381191090366840832.2 x22 - 6x20 + 19x18 - 15x16 - 90x14 + 259x12 - 217x10 + 142x8 - 495x6 + 761x4 - 501x2 + 167 \( -\,2^{22}\cdot 167^{11} \) 22T29 Trivial (GRH)
22.0.13329203788379546293009624459083.1 x22 - x21 + 8x20 + x19 + 33x18 + 20x17 + 97x16 + 111x15 + 195x14 + 258x13 + 328x12 + 369x11 + 392x10 + 323x9 + 362x8 + 155x7 + 199x6 + 67x5 + 63x4 + 12x3 + 11x2 + 2x + 1 \( -\,3^{11}\cdot 8674315276967^{2} \) 22T47 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)
22.0.22378993818717495955548767565627.1 x22 - 2x21 + 3x20 + 8x19 - 22x18 + 38x17 - 4x16 - 57x15 + 146x14 - 127x13 + 42x12 + 144x11 - 154x10 + 123x9 - 19x8 - 35x7 + 41x6 - 58x5 + 35x4 - 12x3 + 7x2 - 2x + 1 \( -\,3^{11}\cdot 1831^{8} \) 22T13 Trivial (GRH)
22.0.22378993818717495955548767565627.2 x22 - 2x21 + x20 - 10x19 + 18x18 + 2x17 + 31x16 - 76x15 - 19x14 - 8x13 + 188x12 - 50x11 - 76x10 - 135x9 + 130x8 + 29x7 + 42x6 - 76x5 + 11x4 - 8x3 + 13x2 - 4x + 1 \( -\,3^{11}\cdot 1831^{8} \) 22T13 Trivial (GRH)
22.0.191943424957750480504146841291811.1 x22 - 11x21 + 66x20 - 275x19 + 847x18 - 1980x17 + 3454x16 - 4070x15 + 1100x14 + 9482x13 - 30690x12 + 60224x11 - 77803x10 + 49665x9 + 48642x8 - 188375x7 + 271315x6 - 233860x5 + 132748x4 - 52624x3 + 14960x2 - 2816x + 256 \( -\,11^{31} \) $D_{11}$ (as 22T2) Trivial (GRH)
22.0.349622146420960826774166244950016.1 x22 - 2x11 + 2 \( -\,2^{32}\cdot 11^{22} \) $C_2\times F_{11}$ (as 22T6) Trivial (GRH)
22.0.529866739430089519756710630129664.1 x22 + 8x20 + 29x18 + 99x16 + 222x14 + 344x12 + 382x10 + 254x8 + 145x6 + 84x4 + 32x2 + 9 \( -\,2^{22}\cdot 1831^{8} \) 22T42 Trivial (GRH)
22.0.529866739430089519756710630129664.2 x22 + 5x20 - 3x18 - 2x16 + 35x14 - 32x12 + 18x10 + 19x8 - 11x6 + 5x4 + 7x2 + 1 \( -\,2^{22}\cdot 1831^{8} \) 22T42 Trivial (GRH)
22.0.5354138939812686410506736146606791.1 x22 + 22x20 + 209x18 + 1122x16 + 3740x14 + 8008x12 - x11 + 11011x10 - 11x9 + 9438x8 - 44x7 + 4719x6 - 77x5 + 1210x4 - 55x3 + 121x2 - 11x + 1 \( -\,3^{11}\cdot 11^{22}\cdot 13^{5} \) 22T20 Trivial (GRH)
22.0.8866351725365604006246875731591168.1 x22 - 22x20 + 209x18 - 1122x16 + 3740x14 - 8008x12 - 6x11 + 11011x10 + 66x9 - 9438x8 - 264x7 + 4719x6 + 462x5 - 1210x4 - 330x3 + 121x2 + 66x + 10 \( -\,2^{32}\cdot 11^{18}\cdot 13^{5} \) 22T20 Trivial (GRH)
22.0.13340299673339979463335491965812736.1 x22 - 4x + 4 \( -\,2^{22}\cdot 195359\cdot 16280669397912337149101 \) 22T59 Trivial (GRH)
22.0.61533497770089105512253259111202816.1 x22 - 11x20 + 33x18 - 66x17 - 44x16 + 308x15 + 253x14 - 44x13 + 913x12 + 1840x11 + 1309x10 - 814x9 + 2904x8 + 4752x7 + 7117x6 - 4004x5 + 825x4 - 44x3 + 6721x2 - 5434x + 1644 \( -\,2^{36}\cdot 11^{23} \) 22T14 Trivial (GRH)
22.0.81311754447107557425705345638989824.1 x22 + 9 \( -\,2^{22}\cdot 3^{20}\cdot 11^{18} \) $C_2\times F_{11}$ (as 22T6) Trivial (GRH)
22.0.366768227637345227672179097600000000.1 x22 - 11x21 + 55x20 - 154x19 + 187x18 + 363x17 - 2255x16 + 5016x15 - 5082x14 - 2046x13 + 13442x12 - 15368x11 + 6358x10 - 33242x9 + 159434x8 - 361944x7 + 546073x6 - 684519x5 + 779031x4 - 754798x3 + 577951x2 - 314545x + 86485 \( -\,2^{20}\cdot 5^{8}\cdot 11^{23} \) 22T14 Trivial (GRH)
22.0.618003811463870173100056726923640832.1 x22 - 8x + 8 \( -\,2^{24}\cdot 37811\cdot 73885382563\cdot 13185438208339 \) 22T59 Trivial (GRH)
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