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Label Polynomial Discriminant Galois group Class group Regulator
8.0.19327352832.9 $x^{8} + 8 x^{4} - 8 x^{2} + 2$ $2^{31}\cdot 3^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $215.192281138$
8.0.362924736512.2 $x^{8} + 8 x^{6} + 32 x^{4} + 56 x^{2} + 18$ $2^{31}\cdot 13^{2}$ $C_2 \wr S_4$ (as 8T44) $[4]$ $147.307341843$
8.4.362924736512.3 $x^{8} - 8 x^{4} - 8 x^{2} + 2$ $2^{31}\cdot 13^{2}$ $C_2 \wr S_4$ (as 8T44) trivial $1342.41933514$
8.0.775241596928.11 $x^{8} - 16 x^{6} + 88 x^{4} - 184 x^{2} + 162$ $2^{31}\cdot 19^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $1836.94636985$
8.0.2338609692672.40 $x^{8} + 16 x^{6} + 72 x^{4} + 72 x^{2} + 162$ $2^{31}\cdot 3^{2}\cdot 11^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $1355.13942761$
8.0.2338609692672.47 $x^{8} + 8 x^{6} + 112 x^{4} + 264 x^{2} + 242$ $2^{31}\cdot 3^{2}\cdot 11^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[6]$ $464.123808905$
8.0.3970697265152.7 $x^{8} + 8 x^{6} + 16 x^{4} - 40 x^{2} + 18$ $2^{31}\cdot 43^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $3993.19017044$
8.0.6977174372352.6 $x^{8} - 24 x^{6} + 128 x^{4} + 152 x^{2} + 722$ $2^{31}\cdot 3^{2}\cdot 19^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $1090.06338522$
8.0.6977174372352.11 $x^{8} + 8 x^{6} + 144 x^{4} + 72 x^{2} + 1458$ $2^{31}\cdot 3^{2}\cdot 19^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $3513.24668913$
8.0.10224169648128.4 $x^{8} + 16 x^{6} + 136 x^{4} + 552 x^{2} + 1058$ $2^{31}\cdot 3^{2}\cdot 23^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $860.01586505$
8.0.10224169648128.8 $x^{8} + 24 x^{6} + 272 x^{4} + 1472 x^{2} + 4232$ $2^{31}\cdot 3^{2}\cdot 23^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $1805.2994718$
8.0.21047487234048.1 $x^{8} - 24 x^{6} + 288 x^{4} - 1080 x^{2} + 1458$ $2^{31}\cdot 3^{4}\cdot 11^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $2494.26555939$
8.0.21047487234048.7 $x^{8} + 32 x^{6} + 232 x^{4} - 264 x^{2} + 2178$ $2^{31}\cdot 3^{4}\cdot 11^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $1004.79192912$
8.0.31441308090368.4 $x^{8} + 32 x^{6} + 344 x^{4} + 1144 x^{2} + 2178$ $2^{31}\cdot 11^{4}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $18349.8261497$
8.0.41491531563008.2 $x^{8} + 8 x^{6} + 48 x^{4} + 392 x^{2} + 1458$ $2^{31}\cdot 139^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3]$ $1196.32058164$
8.0.46404974149632.38 $x^{8} + 392 x^{4} + 2744 x^{2} + 4802$ $2^{31}\cdot 3^{2}\cdot 7^{4}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $2860.24379556$
8.0.50270444716032.1 $x^{8} + 8 x^{6} + 352 x^{4} - 2856 x^{2} + 5202$ $2^{31}\cdot 3^{4}\cdot 17^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $1722.48615446$
8.0.50270444716032.3 $x^{8} + 40 x^{6} + 448 x^{4} + 408 x^{2} + 5202$ $2^{31}\cdot 3^{4}\cdot 17^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $3679.06819596$
8.0.57056493043712.12 $x^{8} + 72 x^{4} + 24 x^{2} + 2$ $2^{31}\cdot 163^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[5]$ $3879.01824985$
8.0.61334280470528.3 $x^{8} - 8 x^{6} - 416 x^{4} + 4576 x^{2} + 1352$ $2^{31}\cdot 13^{4}$ $C_2 \wr S_4$ (as 8T44) $[14]$ $1363.5894066$
8.4.61334280470528.12 $x^{8} + 40 x^{6} + 416 x^{4} - 936 x^{2} + 338$ $2^{31}\cdot 13^{4}$ $C_2 \wr S_4$ (as 8T44) trivial $32230.6457932$
8.0.62794569351168.9 $x^{8} - 16 x^{6} + 568 x^{4} - 3192 x^{2} + 6498$ $2^{31}\cdot 3^{4}\cdot 19^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $1884.93609732$
8.0.108716359680000.4 $x^{8} + 40 x^{6} + 400 x^{4} - 3000 x^{2} + 11250$ $2^{31}\cdot 3^{4}\cdot 5^{4}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $3796.8748132$
8.0.110657684897792.9 $x^{8} - 16 x^{6} + 136 x^{4} - 216 x^{2} + 162$ $2^{31}\cdot 227^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $16812.0063797$
8.4.126806761930752.7 $x^{8} + 8 x^{6} - 72 x^{2} + 18$ $2^{31}\cdot 3^{10}$ $C_2 \wr S_4$ (as 8T44) trivial $69298.3332102$
8.4.126806761930752.15 $x^{8} + 8 x^{6} - 56 x^{2} + 50$ $2^{31}\cdot 3^{10}$ $C_2 \wr S_4$ (as 8T44) trivial $44134.9515991$
8.4.128902705971200.2 $x^{8} - 8 x^{6} - 16 x^{5} - 32 x^{4} + 64 x^{3} + 200 x^{2} - 64 x - 110$ $2^{31}\cdot 5^{2}\cdot 7^{4}$ $S_4\wr C_2$ (as 8T47) trivial $48999.667307$
8.0.162403450880000.4 $x^{8} + 40 x^{6} + 800 x^{4} + 5000 x^{2} + 11250$ $2^{31}\cdot 5^{4}\cdot 11^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $12138.0355028$
8.0.171989817884672.4 $x^{8} + 8 x^{6} + 96 x^{4} + 56 x^{2} + 18$ $2^{31}\cdot 283^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $18442.7719682$
8.0.202398186340352.12 $x^{8} + 16 x^{6} + 120 x^{4} + 40 x^{2} + 162$ $2^{31}\cdot 307^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $31334.3143362$
8.0.282971772813312.11 $x^{8} - 24 x^{6} + 848 x^{4} - 7656 x^{2} + 19602$ $2^{31}\cdot 3^{2}\cdot 11^{4}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 4]$ $7692.52288894$
8.0.417644767346688.30 $x^{8} + 40 x^{6} + 688 x^{4} + 5592 x^{2} + 19602$ $2^{31}\cdot 3^{4}\cdot 7^{4}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 6]$ $5800.08940292$
8.0.417644767346688.34 $x^{8} + 8 x^{6} + 208 x^{4} - 72 x^{2} + 18$ $2^{31}\cdot 3^{4}\cdot 7^{4}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 6]$ $2946.10297816$
8.0.421441518436352.3 $x^{8} - 24 x^{6} + 224 x^{4} - 792 x^{2} + 1458$ $2^{31}\cdot 443^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $52364.9336355$
8.0.468342561308672.5 $x^{8} + 16 x^{6} + 56 x^{4} - 184 x^{2} + 162$ $2^{31}\cdot 467^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $56121.9793053$
8.0.517717505343488.1 $x^{8} + 8 x^{6} + 48 x^{4} - 40 x^{2} + 722$ $2^{31}\cdot 491^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[3]$ $10765.1078728$
8.2.536971843731456.21 $x^{8} + 120 x^{4} + 376 x^{2} - 126$ $-\,2^{31}\cdot 3^{6}\cdot 7^{3}$ $C_2 \wr S_4$ (as 8T44) $[2]$ $22862.2471917$
8.2.536971843731456.26 $x^{8} + 8 x^{6} - 96 x^{4} + 224 x^{2} - 56$ $-\,2^{31}\cdot 3^{6}\cdot 7^{3}$ $C_2 \wr S_4$ (as 8T44) trivial $109798.426479$
8.2.536971843731456.42 $x^{8} - 8 x^{6} - 96 x^{4} + 1120 x^{2} - 2744$ $-\,2^{31}\cdot 3^{6}\cdot 7^{3}$ $C_2 \wr S_4$ (as 8T44) $[2]$ $23073.3324381$
8.2.536971843731456.45 $x^{8} + 8 x^{6} + 240 x^{4} - 616 x^{2} - 686$ $-\,2^{31}\cdot 3^{6}\cdot 7^{3}$ $C_2 \wr S_4$ (as 8T44) $[2]$ $70376.6618457$
8.2.536971843731456.51 $x^{8} - 24 x^{6} + 144 x^{4} - 256 x^{2} - 504$ $-\,2^{31}\cdot 3^{6}\cdot 7^{3}$ $C_2 \wr S_4$ (as 8T44) $[6]$ $29808.2688754$
8.2.536971843731456.54 $x^{8} + 8 x^{6} - 48 x^{4} - 504$ $-\,2^{31}\cdot 3^{6}\cdot 7^{3}$ $C_2 \wr S_4$ (as 8T44) trivial $176634.525312$
8.0.680685744422912.1 $x^{8} - 16 x^{6} + 344 x^{4} - 1400 x^{2} + 6498$ $2^{31}\cdot 563^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $200312.620751$
8.4.690392370511872.3 $x^{8} - 24 x^{6} + 432 x^{4} - 1944 x^{2} + 1458$ $2^{31}\cdot 3^{8}\cdot 7^{2}$ $C_2 \wr S_4$ (as 8T44) $[2]$ $129960.187894$
8.0.690392370511872.10 $x^{8} + 24 x^{6} + 96 x^{4} + 96 x^{2} + 72$ $2^{31}\cdot 3^{8}\cdot 7^{2}$ $C_2 \wr S_4$ (as 8T44) $[2, 12]$ $1737.44868921$
8.0.694567078723584.11 $x^{8} - 56 x^{6} + 880 x^{4} - 2904 x^{2} + 7986$ $2^{31}\cdot 3^{5}\cdot 11^{3}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $16545.0759534$
8.0.694567078723584.16 $x^{8} + 40 x^{6} + 544 x^{4} + 3048 x^{2} + 7986$ $2^{31}\cdot 3^{5}\cdot 11^{3}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $12193.4469004$
8.0.694567078723584.17 $x^{8} + 8 x^{6} - 272 x^{4} - 936 x^{2} + 23826$ $2^{31}\cdot 3^{5}\cdot 11^{3}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $11505.4146672$
8.0.694567078723584.44 $x^{8} - 24 x^{6} + 192 x^{4} - 72 x^{2} + 594$ $2^{31}\cdot 3^{5}\cdot 11^{3}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $7687.49247722$
8.0.700167716077568.3 $x^{8} - 24 x^{6} + 160 x^{4} - 104 x^{2} + 18$ $2^{31}\cdot 571^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $69848.8089726$
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