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Label Polynomial Discriminant Galois group Class group
16.0.72057594037927936.1 x16 - 4x12 + 22x8 - 4x4 + 1 \( 2^{56} \) $C_2^2.D_4$ (as 16T33) trivial
16.0.288230376151711744.3 x16 - 8x14 + 32x12 - 104x10 + 194x8 - 104x6 + 32x4 - 8x2 + 1 \( 2^{58} \) $C_2^2.D_4$ (as 16T33) trivial
16.0.530...000.1 x16 + 4x14 - 4x10 + 34x8 - 4x6 + 4x2 + 1 \( 2^{28}\cdot 3^{4}\cdot 5^{12} \) $C_2^2.D_4$ (as 16T33) $[2]$
16.0.530...000.2 x16 - 4x15 + 8x14 - 16x13 + 8x12 + 16x11 + 20x9 - 14x8 - 20x7 - 16x5 + 8x4 + 16x3 + 8x2 + 4x + 1 \( 2^{28}\cdot 3^{4}\cdot 5^{12} \) $C_2^2.D_4$ (as 16T33) $[2]$
16.0.107...000.3 x16 - 8x15 + 28x14 - 52x13 + 36x12 + 68x11 - 204x10 + 228x9 - 61x8 - 188x7 + 348x6 - 340x5 + 228x4 - 108x3 + 36x2 - 8x + 1 \( 2^{40}\cdot 5^{10} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.107...000.5 x16 - 8x15 + 32x14 - 84x13 + 174x12 - 308x11 + 444x10 - 476x9 + 377x8 - 252x7 + 216x6 - 268x5 + 292x4 - 164x3 + 24x2 + 5 \( 2^{40}\cdot 5^{10} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.171...000.2 x16 - 6x15 + 16x14 - 24x13 + 20x12 - 6x11 + 12x10 - 30x9 + 59x8 - 30x7 + 12x6 - 6x5 + 20x4 - 24x3 + 16x2 - 6x + 1 \( 2^{28}\cdot 3^{8}\cdot 5^{10} \) $C_2^2.D_4$ (as 16T33) $[2]$
16.0.171...000.3 x16 - 8x14 + 24x12 + 16x10 + 24x8 - 8x6 + 56x4 + 100 \( 2^{28}\cdot 3^{8}\cdot 5^{10} \) $C_2^2.D_4$ (as 16T33) $[2]$
16.0.779...625.1 x16 + 7x14 - 14x12 - 8x10 + 29x8 - 8x6 - 14x4 + 7x2 + 1 \( 5^{10}\cdot 41^{8} \) $C_2^2.D_4$ (as 16T33) trivial
16.0.119...144.8 x16 - 2x15 + x14 + 8x13 - 40x12 + 56x11 - 24x10 - 112x9 + 383x8 - 598x7 + 723x6 - 544x5 + 384x4 - 104x3 + 92x2 + 32 \( 2^{34}\cdot 17^{8} \) $C_2^2.D_4$ (as 16T33) trivial
16.0.119...144.9 x16 - 8x15 + 28x14 - 56x13 + 70x12 - 56x11 + 144x10 - 588x9 + 1190x8 - 1276x7 + 754x6 - 232x5 + 61x4 - 64x3 + 48x2 - 16x + 2 \( 2^{34}\cdot 17^{8} \) $C_2^2.D_4$ (as 16T33) trivial
16.0.268...000.2 x16 - 4x15 + 4x14 + 16x13 - 36x12 - 76x11 + 408x10 - 712x9 + 691x8 - 460x7 + 368x6 - 312x5 + 204x4 - 40x3 + 8x + 1 \( 2^{40}\cdot 5^{12} \) $C_2^2.D_4$ (as 16T33) $[2]$
16.0.268...000.4 x16 - 8x15 + 40x14 - 140x13 + 386x12 - 860x11 + 1576x10 - 2380x9 + 3001x8 - 3180x7 + 2820x6 - 2052x5 + 1196x4 - 540x3 + 180x2 - 40x + 5 \( 2^{40}\cdot 5^{12} \) $C_2^2.D_4$ (as 16T33) $[2]$
16.0.164...729.3 x16 - 4x15 + 4x14 + 9x13 - 16x12 - 16x11 + 23x10 + 140x9 - 222x8 - 317x7 + 1076x6 - 632x5 - 455x4 + 462x3 + 36x2 - 88x + 16 \( 13^{8}\cdot 17^{10} \) $C_2^2.D_4$ (as 16T33) trivial
16.0.187...625.2 x16 - 4x15 + 10x14 - 20x13 + 62x12 - 178x11 + 410x10 - 710x9 + 1146x8 - 1668x7 + 2314x6 - 2822x5 + 3045x4 - 2574x3 + 1860x2 - 872x + 304 \( 5^{10}\cdot 61^{8} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.8.194...625.1 x16 - 5x14 - 16x12 + 25x10 + 71x8 + 25x6 - 16x4 - 5x2 + 1 \( 5^{12}\cdot 41^{8} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.255...409.3 x16 - 8x15 + 32x14 - 78x13 + 130x12 - 166x11 + 268x10 - 514x9 + 565x8 - 540x7 - 202x6 + 1084x5 + 85x4 + 444x3 + 1221x2 + 666x + 111 \( 3^{12}\cdot 37^{10} \) $C_2^2.D_4$ (as 16T33) $[4]$
16.0.216...625.5 x16 - 6x15 + 11x14 + 12x13 - 79x12 + 124x11 + 8x10 - 32x9 - 687x8 + 934x7 + 1800x6 - 11022x5 + 27126x4 - 37120x3 + 32730x2 - 21280x + 8105 \( 5^{10}\cdot 19^{12} \) $C_2^2.D_4$ (as 16T33) $[4]$ (GRH)
16.8.468...625.1 x16 + 5x14 - 31x12 - 50x10 + 166x8 - 50x6 - 31x4 + 5x2 + 1 \( 5^{12}\cdot 61^{8} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.689...889.2 x16 - 4x15 + 20x14 - 75x13 + 234x12 - 586x11 + 1265x10 - 2228x9 + 3366x8 - 4331x7 + 5144x6 - 5434x5 + 5155x4 - 3820x3 + 2452x2 - 1328x + 368 \( 13^{10}\cdot 29^{8} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.102...625.4 x16 - 3x15 - 7x14 + 11x13 + 113x12 - 226x11 - 143x10 - 199x9 + 3108x8 - 4526x7 + 1698x6 - 7747x5 + 27621x4 - 35200x3 + 18760x2 - 3400x + 400 \( 5^{12}\cdot 29^{10} \) $C_2^2.D_4$ (as 16T33) $[4]$ (GRH)
16.0.102...625.6 x16 - 7x15 + 23x14 - 50x13 + 115x12 - 263x11 + 384x10 - 245x9 + 289x8 - 890x7 + 1101x6 - 1581x5 + 3875x4 - 7140x3 + 8532x2 - 5184x + 1296 \( 5^{12}\cdot 29^{10} \) $C_2^2.D_4$ (as 16T33) $[4]$ (GRH)
16.8.105...625.3 x16 - 10x14 - 9x12 + 105x10 + 111x8 - 420x6 - 114x4 - 65x2 + 1 \( 5^{10}\cdot 101^{8} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.379...041.4 x16 - 5x15 - 4x14 + 57x13 - 83x12 - 193x11 + 1042x10 - 682x9 - 1226x8 + 1038x7 - 5305x6 + 4294x5 + 6685x4 + 1566x3 + 8184x2 - 9072x + 2352 \( 3^{12}\cdot 61^{10} \) $C_2^2.D_4$ (as 16T33) $[4]$ (GRH)
16.0.475...681.1 x16 - 7x14 - x12 + 67x10 + 136x8 + 67x6 - x4 - 7x2 + 1 \( 13^{8}\cdot 17^{12} \) $C_2^2.D_4$ (as 16T33) $[4]$ (GRH)
16.0.490...824.1 x16 + 24x14 + 224x12 + 1044x10 + 2629x8 + 3612x6 + 2536x4 + 712x2 + 4 \( 2^{46}\cdot 17^{8} \) $C_2^2.D_4$ (as 16T33) $[2, 2, 4]$ (GRH)
16.16.490...824.1 x16 - 24x14 + 224x12 - 1044x10 + 2629x8 - 3612x6 + 2536x4 - 712x2 + 4 \( 2^{46}\cdot 17^{8} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.540...625.2 x16 + 15x14 + 106x12 + 475x10 + 1486x8 + 3230x6 + 4576x4 + 3715x2 + 1296 \( 5^{12}\cdot 19^{12} \) $C_2^2.D_4$ (as 16T33) $[2, 8]$ (GRH)
16.0.264...625.12 x16 - 8x14 + 78x12 + 94x10 - 295x8 + 54x6 + 2413x4 - 3573x2 + 3136 \( 5^{12}\cdot 101^{8} \) $C_2^2.D_4$ (as 16T33) $[2, 2, 4]$ (GRH)
16.0.345...625.6 x16 - 2x15 + 6x14 + 8x13 + 9x12 + 62x11 + 657x10 - 416x9 - 2247x8 + 2722x7 + 5093x6 - 5996x5 - 1956x4 + 5684x3 - 2001x2 - 1624x + 1856 \( 5^{10}\cdot 29^{12} \) $C_2^2.D_4$ (as 16T33) $[3, 12]$ (GRH)
16.0.345...625.8 x16 - 3x15 - 3x14 + 12x13 - 19x12 + 100x11 - 70x10 + 95x9 - 90x8 - 1065x7 + 3906x6 - 6078x5 + 6817x4 - 7738x3 + 11971x2 - 13835x + 7295 \( 5^{10}\cdot 29^{12} \) $C_2^2.D_4$ (as 16T33) $[3, 12]$ (GRH)
16.0.349...921.2 x16 - 8x15 + 18x14 + 14x13 - 75x12 - 96x11 + 301x10 + 662x9 + 198x8 - 8108x7 + 11425x6 + 360x5 - 3372x4 - 6392x3 + 2064x2 + 3008x + 4288 \( 3^{12}\cdot 37^{12} \) $C_2^2.D_4$ (as 16T33) $[2, 8]$ (GRH)
16.8.858...489.4 x16 - 6x15 + x14 + 49x13 - 141x12 + 33x11 + 813x10 - 1008x9 - 149x8 + 5648x7 - 1418x6 - 9723x5 - 331x4 + 5028x3 + 192x2 - 728x + 208 \( 13^{10}\cdot 53^{8} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.8.116...241.1 x16 - 2x15 + 2x14 - 33x13 + 53x12 + 83x11 - 77x10 + 51x9 - 1774x8 + 1850x7 + 5383x6 - 6162x5 - 5048x4 + 6520x3 + 992x2 - 3360x - 576 \( 13^{12}\cdot 29^{8} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.16.119...000.1 x16 - 8x15 + 4x14 + 112x13 - 254x12 - 296x11 + 1457x10 - 949x9 - 1463x8 + 1998x7 - 97x6 - 807x5 + 256x4 + 86x3 - 39x2 - x + 1 \( 2^{8}\cdot 5^{12}\cdot 61^{8} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.119...000.1 x16 - 8x15 + 34x14 - 78x13 + 166x12 - 296x11 + 592x10 - 1594x9 + 3932x8 - 9382x7 + 20318x6 - 34912x5 + 44991x4 - 39494x3 + 23226x2 - 7276x + 1076 \( 2^{8}\cdot 5^{12}\cdot 61^{8} \) $C_2^2.D_4$ (as 16T33) $[2, 2, 4]$ (GRH)
16.8.264...569.5 x16 - 8x15 + 8x14 + 84x13 - 150x12 - 556x11 + 938x10 + 3362x9 - 5172x8 - 10748x7 + 17454x6 + 10916x5 - 19717x4 - 3822x3 - 9984x2 + 17394x + 9763 \( 13^{10}\cdot 61^{8} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.8.431...625.2 x16 - 4x15 - 10x14 + 127x13 - 380x12 - 84x11 + 890x10 + 591x9 - 2244x8 - 1586x7 + 3018x6 + 2649x5 - 501x4 - 2078x3 - 204x2 + 520x - 80 \( 5^{8}\cdot 101^{10} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.469...969.7 x16 - 8x15 + 58x14 - 266x13 + 1023x12 - 3044x11 + 7385x10 - 14408x9 + 21952x8 - 25692x7 + 20601x6 - 8502x5 - 1564x4 + 4240x3 + 11504x2 - 13280x + 8128 \( 13^{12}\cdot 17^{10} \) $C_2^2.D_4$ (as 16T33) $[2]$ (GRH)
16.0.480...689.6 x16 - 4x15 + 4x14 - 11x12 + 214x11 - 181x10 - 506x9 + 1977x8 - 954x7 + 2107x6 + 10450x5 - 16x4 + 934x3 + 20095x2 + 18530x + 5644 \( 17^{10}\cdot 47^{8} \) $C_2^2.D_4$ (as 16T33) $[20]$ (GRH)
16.0.924...625.2 x16 + 23x14 + 276x12 + 2818x10 + 20250x8 + 86927x6 + 243976x4 + 501552x2 + 531441 \( 5^{8}\cdot 109^{10} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.8.142...329.5 x16 - 30x14 + 367x12 - 2637x10 + 10547x8 - 19670x6 + 14277x4 - 2912x2 + 256 \( 13^{8}\cdot 53^{10} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.220...625.5 x16 - 2x15 - 17x14 + 36x13 + 141x12 - 438x11 + 255x10 + 2168x9 - 6440x8 - 7008x7 + 45751x6 + 10856x5 - 121567x4 - 41412x3 + 98626x2 + 66550x + 52645 \( 5^{10}\cdot 41^{12} \) $C_2^2.D_4$ (as 16T33) $[2]$ (GRH)
16.8.581...321.5 x16 - 18x14 + 127x12 - 875x10 + 4047x8 - 17612x6 + 47142x4 - 37341x2 + 6561 \( 13^{8}\cdot 61^{10} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.818...809.6 x16 - 8x14 - x13 + 54x12 + 210x11 + 209x10 - 589x9 - 630x8 + 1721x7 + 4011x6 + 14085x5 + 52958x4 + 81624x3 + 79362x2 + 77319x + 77291 \( 17^{10}\cdot 67^{8} \) $C_2^2.D_4$ (as 16T33) $[4]$ (GRH)
16.0.105...681.9 x16 - 2x14 + 45x12 - 53x10 + 3834x8 - 1653x6 + 7748x4 - 2304x2 + 65536 \( 23^{8}\cdot 41^{10} \) $C_2^2.D_4$ (as 16T33) $[12]$ (GRH)
16.0.141...561.3 x16 - x15 - x14 + 12x13 - 79x12 + 484x11 + 1411x10 - 1635x9 + 4582x8 + 35484x7 + 84259x6 + 65558x5 - 12802x4 + 8304x3 + 328913x2 + 621070x + 515524 \( 3^{12}\cdot 61^{12} \) $C_2^2.D_4$ (as 16T33) $[2, 8]$ (GRH)
16.0.145...641.16 x16 - 8x15 + 8x14 + 38x13 + 161x12 - 974x11 + 765x10 + 324x9 + 5385x8 - 23710x7 + 72233x6 - 187868x5 + 360296x4 - 475942x3 + 424309x2 - 225810x + 52092 \( 13^{12}\cdot 53^{8} \) $C_2^2.D_4$ (as 16T33) $[2, 4, 8]$ (GRH)
16.0.210...625.1 x16 - 4x15 + 56x14 - 182x13 + 1092x12 - 3072x11 + 9994x10 - 20362x9 + 40781x8 - 34526x7 + 13090x6 + 38884x5 + 15301x4 - 14428x3 + 40421x2 + 9424x + 27869 \( 5^{8}\cdot 149^{10} \) $C_2^2.D_4$ (as 16T33) trivial (GRH)
16.0.242...849.4 x16 - 6x15 - 6x14 + 44x13 + 162x12 - 479x11 - 287x10 + 2522x9 + 3180x8 - 9028x7 - 10699x6 + 401x5 + 17424x4 + 6594x3 + 99876x2 - 192542x + 220367 \( 7^{12}\cdot 53^{10} \) $C_2^2.D_4$ (as 16T33) $[4]$ (GRH)
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