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Label Polynomial Discriminant Galois group Class group
22.2.707...496.1 x22 - 3x20 + x18 + x16 + 6x14 - 8x12 + 5x6 - x2 - 1 \( 2^{22}\cdot 167^{10} \) 22T30 trivial (GRH)
22.2.707...496.2 x22 - 6x20 + 15x18 - 27x16 + 57x14 - 109x12 + 140x10 - 129x8 + 89x6 - 41x4 + 10x2 - 1 \( 2^{22}\cdot 167^{10} \) 22T30 trivial (GRH)
22.10.226...241.1 x22 - 2x21 - 21x20 + 53x19 - 10x18 + 194x17 - 407x16 - 1527x15 + 6220x14 - 4654x13 - 629x12 - 17002x11 + 27165x10 + 61220x9 - 186927x8 + 181221x7 - 68565x6 - 17301x5 + 21983x4 + 305x3 - 3623x2 + 368x + 89 \( 1297^{12} \) 22T30 trivial (GRH)
22.14.226...241.1 x22 - 2x21 - 39x20 + 64x19 + 637x18 - 838x17 - 5728x16 + 5845x15 + 31533x14 - 23266x13 - 111308x12 + 50752x11 + 255873x10 - 41357x9 - 384169x8 - 55415x7 + 364754x6 + 157543x5 - 189895x4 - 128323x3 + 35550x2 + 35218x + 3037 \( 1297^{12} \) 22T30 $[2]$ (GRH)
22.6.226...241.1 x22 - 10x21 + 29x20 + 3x19 - 188x18 + 381x17 + 73x16 - 825x15 - 72x14 + 1868x13 - 351x12 + 2371x11 + 18854x10 + 14453x9 + 97552x8 + 172564x7 + 165961x6 + 92915x5 + 32329x4 + 6644x3 + 718x2 + 72x + 5 \( 1297^{12} \) 22T30 $[2]$ (GRH)
22.10.226...241.2 x22 - x21 - 15x20 + 49x19 + 44x18 - 485x17 + 631x16 + 1475x15 - 5443x14 + 3138x13 + 10542x12 - 20731x11 + 9385x10 - 1329x9 + 26060x8 - 12671x7 - 46031x6 + 81808x5 - 90460x4 + 26591x3 + 21718x2 - 4276x - 289 \( 1297^{12} \) 22T30 $[2]$ (GRH)
22.14.226...241.2 x22 - 3x21 - 24x20 + 59x19 + 273x18 - 436x17 - 1924x16 + 1356x15 + 5010x14 + 14999x13 - 9512x12 - 114771x11 + 18405x10 + 290616x9 + 69522x8 - 375325x7 - 259853x6 + 293924x5 + 260945x4 - 133418x3 - 93266x2 + 21174x + 11623 \( 1297^{12} \) 22T30 $[2]$ (GRH)
22.6.226...241.2 x22 - x21 - 11x20 + 37x19 - 125x18 - 206x17 + 947x16 - 1002x15 + 693x14 - 867x13 - 2005x12 + 50723x11 - 26677x10 - 11638x9 + 87302x8 + 129837x7 + 279630x6 - 109510x5 - 453150x4 - 37802x3 + 155367x2 - 17135x - 36319 \( 1297^{12} \) 22T30 trivial (GRH)
22.10.226...241.3 x22 - x21 - x20 + 60x19 - 104x18 - 389x17 + 930x16 + 1131x15 - 4806x14 - 200x13 + 14407x12 - 16040x11 - 4755x10 + 43121x9 - 59207x8 - 13398x7 + 79635x6 - 16708x5 - 39710x4 - 1394x3 + 28884x2 - 12840x + 1343 \( 1297^{12} \) 22T30 trivial (GRH)
22.14.226...241.3 x22 - 7x21 - 9x20 + 171x19 - 276x18 - 1022x17 + 3668x16 - 1134x15 - 10988x14 + 19765x13 - 17789x12 + 6x11 + 111532x10 - 268518x9 - 21573x8 + 707388x7 - 501170x6 - 789327x5 + 795886x4 + 400629x3 - 428800x2 - 69431x + 68279 \( 1297^{12} \) 22T30 trivial (GRH)
22.10.226...241.4 x22 - 35x20 - 72x19 + 349x18 + 1479x17 + 303x16 - 6784x15 - 5684x14 + 33196x13 + 87806x12 + 64287x11 - 46217x10 - 105124x9 - 72109x8 - 28967x7 + 30762x6 + 56113x5 - 4944x4 - 27192x3 - 1892x2 + 3210x + 509 \( 1297^{12} \) 22T30 trivial (GRH)
22.14.226...241.4 x22 - 4x21 - 15x20 + 64x19 + 79x18 - 540x17 + 528x16 + 1865x15 - 4894x14 - 1811x13 + 8981x12 + 4163x11 - 6857x10 - 8000x9 + 2421x8 + 4419x7 - 158x6 - 547x5 - 172x4 - 39x3 + 52x2 - 2x - 1 \( 1297^{12} \) 22T30 $[2]$ (GRH)
22.10.226...241.5 x22 - 5x21 + 6x20 + 16x19 - 102x18 + 158x17 + 126x16 - 120x15 + 3303x14 - 15009x13 - 7047x12 + 123140x11 - 153297x10 - 373493x9 + 984859x8 + 258716x7 - 2326169x6 + 706632x5 + 2505600x4 - 1023169x3 - 1195624x2 + 155028x + 13045 \( 1297^{12} \) 22T30 trivial (GRH)
22.10.226...241.6 x22 - 5x21 + x20 + 45x19 - 310x18 + 927x17 - 1531x16 + 1204x15 + 2550x14 - 9408x13 + 18565x12 - 24332x11 + 23469x10 + 9560x9 - 46190x8 + 69717x7 - 91965x6 + 67098x5 - 36153x4 + 9787x3 + 1002x2 - 474x - 25 \( 1297^{12} \) 22T30 $[2]$ (GRH)
22.10.565...896.1 x22 - 5x20 - 97x18 - 162x16 + 392x14 + 639x12 - 299x10 - 637x8 - 27x6 + 178x4 + 43x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.14.565...896.1 x22 - 6x20 - 8x18 + 116x16 - 174x14 - 339x12 + 1060x10 - 606x8 - 386x6 + 335x4 + 7x2 - 25 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.18.565...896.1 x22 - 16x20 + 46x18 + 155x16 - 748x14 + 688x12 + 579x10 - 1382x8 + 904x6 - 253x4 + 28x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.2.565...896.1 x22 + 17x20 + 116x18 + 402x16 + 715x14 + 475x12 - 392x10 - 919x8 - 646x6 - 207x4 - 28x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.6.565...896.1 x22 + 26x20 + 246x18 + 992x16 + 1270x14 - 1382x12 - 3114x10 - 1149x8 + 264x6 + 117x4 - 5x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.10.565...896.2 x22 - 2x20 - 56x18 + 245x16 + 126x14 - 1903x12 + 1997x10 + 1141x8 - 1026x6 - 464x4 - 41x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.14.565...896.2 x22 - 15x20 + 49x18 + 116x16 - 777x14 + 894x12 + 527x10 - 1202x8 + 244x6 + 212x4 - 65x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.18.565...896.2 x22 - 19x20 + 110x18 - 228x16 - 81x14 + 1073x12 - 1656x10 + 934x8 - 71x6 - 67x4 + 16x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.2.565...896.2 x22 + 25x20 + 250x18 + 1243x16 + 2879x14 + 334x12 - 14126x10 - 33691x8 - 35857x6 - 18585x4 - 4105x2 - 289 \( 2^{22}\cdot 1297^{10} \) 22T30 $[3]$ (GRH)
22.6.565...896.2 x22 + 25x20 + 230x18 + 924x16 + 1202x14 - 2380x12 - 9046x10 - 8766x8 - 865x6 + 1915x4 + 68x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.10.565...896.3 x22 + 3x20 - 62x18 - 30x16 + 1121x14 - 1695x12 - 1287x10 + 2870x8 - 170x6 - 456x4 - 65x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.14.565...896.3 x22 - 5x20 - 49x18 + 168x16 + 746x14 - 1298x12 - 2537x10 + 4881x8 + 681x6 - 5264x4 + 3300x2 - 625 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.10.565...896.4 x22 + 4x20 - 69x18 - 366x16 + 420x14 + 3456x12 + 424x10 - 3247x8 - 1390x6 - 35x4 + 28x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.14.565...896.4 x22 - x20 - 23x18 + 27x16 + 145x14 - 193x12 - 240x10 + 421x8 - 162x6 + 9x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.10.565...896.5 x22 + 19x20 + 30x18 - 427x16 - 1235x14 + 833x12 + 3553x10 - 222x8 - 2608x6 - 298x4 + 42x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.10.565...896.6 x22 + 5x20 - 73x18 - 622x16 - 1447x14 - 211x12 + 2816x10 + 1989x8 - 739x6 - 125x4 + 26x2 - 1 \( 2^{22}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.22.170...216.1 x22 - 124x20 + 6605x18 - 198718x16 + 3731509x14 - 45556647x12 + 364652629x10 - 1879790241x8 + 5953201774x6 - 10615623072x4 + 9237457886x2 - 3015217921 \( 2^{22}\cdot 43^{2}\cdot 1277^{2}\cdot 1297^{10} \) 22T30 trivial (GRH)
22.22.170...216.2 x22 - 140x20 + 8475x18 - 291035x16 + 6250874x14 - 87255611x12 + 795482411x10 - 4618766140x8 + 15964116759x6 - 28133091175x4 + 16687617633x2 - 3015217921 \( 2^{22}\cdot 43^{2}\cdot 1277^{2}\cdot 1297^{10} \) 22T30 trivial (GRH)
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