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Label Polynomial Discriminant Galois group Class group Regulator
7.7.13841287201.1 x7 - 21x5 - 21x4 + 91x3 + 112x2 - 84x - 97 $7^{12}$ $C_7$ (as 7T1) trivial $550.88577714$
7.3.3543369523456.3 x7 - 21x5 - 28x4 - 7x3 - 112x2 + 259x + 244 $2^{8}\cdot 7^{12}$ $\GL(3,2)$ (as 7T5) $[7]$ $12405.1123243$
7.3.3543369523456.4 x7 - 21x5 - 70x4 + 238x3 + 1092x2 - 2240x + 736 $2^{8}\cdot 7^{12}$ $\GL(3,2)$ (as 7T5) $[14]$ $6202.55616215$
7.3.645779095649856.3 x7 - 21x5 - 70x4 - 105x3 - 84x2 - 35x + 40818 $2^{6}\cdot 3^{6}\cdot 7^{12}$ $A_7$ (as 7T6) $[7]$ $58386.9611144$
7.3.1148051725599744.1 x7 - 42x5 - 28x4 + 609x3 + 756x2 - 3024x + 864 $2^{10}\cdot 3^{4}\cdot 7^{12}$ $A_7$ (as 7T6) $[7]$ $105789.61343$
7.3.13841287201000000.2 x7 - 2744x2 + 27440 $2^{6}\cdot 5^{6}\cdot 7^{12}$ $A_7$ (as 7T6) $[7]$ $63284.5358524$
7.3.52308106747638336.4 x7 - 84x5 - 420x4 + 5376x3 - 3780x2 - 16156x + 27900 $2^{6}\cdot 3^{10}\cdot 7^{12}$ $\GL(3,2)$ (as 7T5) $[7]$ $539181.587994$
7.3.52308106747638336.6 x7 - 84x5 - 364x4 - 1680x3 + 6720x2 + 77728x + 391638 $2^{6}\cdot 3^{10}\cdot 7^{12}$ $\GL(3,2)$ (as 7T5) $[7]$ $539181.587994$
7.1.247979172729544704.1 x7 - 882x4 + 882x3 - 15876 $-\,2^{13}\cdot 3^{7}\cdot 7^{12}$ $S_7$ (as 7T7) $[7]$ $1346046.93683$
7.1.1313840933532421875.2 x7 - 35x5 - 70x4 + 280x3 + 1232x2 + 1680x - 117325 $-\,3^{5}\cdot 5^{8}\cdot 7^{12}$ $S_7$ (as 7T7) $[7]$ $620527.310781$
7.7.874...849.1 x7 - 903x5 - 11739x4 - 4515x3 + 484008x2 + 1555568x - 609267 $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $80239711.6814$
7.7.874...849.2 x7 - 903x5 - 3311x4 + 256753x3 + 1655500x2 - 20129676x - 154845881 $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $3504328.2978067407$
7.7.874...849.3 x7 - 903x5 - 1204x4 + 218827x3 + 753704x2 - 16141125x - 86614900 $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $2429511482.583454$
7.7.874...849.4 x7 - 903x5 - 15953x4 - 97223x3 - 177590x2 + 46956x + 94471 $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $8351632.841147239$
7.7.874...849.5 x7 - 903x5 - 3311x4 + 206185x3 + 1491154x2 - 1773492x + 461089 $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $4703614.757954623$
7.7.874...849.6 x7 - 903x5 - 7525x4 + 105049x3 + 905408x2 - 1520652x + 545369 $7^{12}\cdot 43^{6}$ $C_7$ (as 7T1) $[7]$ $12027627.652134134$
8.4.3543369523456.1 x8 - 7x6 - 14x5 + 7x4 + 28x2 + 48x + 14 $2^{8}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) trivial $7262.24637552$
8.0.14173478093824.1 x8 + 7x6 + 21x4 - 14x3 + 42x2 - 48x + 28 $2^{10}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $1447.05229669$
8.0.226775649501184.4 x8 - 2x7 + 14x6 - 14x5 - 126x4 + 630x3 + 658x2 - 5130x + 10267 $2^{14}\cdot 7^{12}$ $C_2^3:C_7$ (as 8T25) trivial $24239.5513308$
8.0.226775649501184.5 x8 - 2x7 + 14x6 + 84x4 - 112x3 + 28x2 + 188x + 310 $2^{14}\cdot 7^{12}$ $C_2^3:C_7$ (as 8T25) trivial $26620.3609911$
8.0.907102598004736.3 x8 - 56x5 + 7x4 - 84x3 + 770x2 - 116x + 2394 $2^{16}\cdot 7^{12}$ $\PSL(2,7)$ (as 8T37) $[2, 6]$ $10627.578275$
8.0.907102598004736.6 x8 - 56x5 - 70x4 + 224x3 + 672x2 + 264x + 329 $2^{16}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $25714.4903521$
8.4.907102598004736.7 x8 - 28x6 - 84x5 + 133x4 + 1204x3 + 2310x2 + 1224x + 189 $2^{16}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $44501.4858602$
8.0.907102598004736.7 x8 - 4x7 + 14x6 - 28x5 + 70x4 - 84x3 + 378x2 - 124x + 517 $2^{16}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $8070.98128542$
8.0.1803810389321521.1 x8 - 2x7 - 28x6 + 154x5 + 189x4 - 2016x3 + 5278x2 + 2701x + 2949 $7^{12}\cdot 19^{4}$ $C_2^3:C_7$ (as 8T25) $[2, 4]$ $7631.3442133$
8.0.1803810389321521.2 x8 - 4x7 + 35x6 - 42x5 + 329x4 - 14x3 + 2611x2 - 6607x + 3692 $7^{12}\cdot 19^{4}$ $C_2^3:C_7$ (as 8T25) $[2, 4]$ $7306.25989421$
8.0.2296103451199488.1 x8 - 3x7 + 28x6 - 161x5 + 392x4 + 371x3 + 672x2 + 353x + 187 $2^{11}\cdot 3^{4}\cdot 7^{12}$ $\PGL(2,7)$ (as 8T43) $[2]$ $91728.6569631$
8.0.3628410392018944.1 x8 - 4x7 - 56x5 + 196x4 - 224x3 + 1792x2 + 1408x + 1088 $2^{18}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $131688.580848$
8.4.3628410392018944.1 x8 - 4x7 + 28x6 - 196x4 - 784x2 + 2016x - 1008 $2^{18}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) trivial $118573.087895$
8.0.3628410392018944.3 x8 - 4x7 + 28x6 - 56x5 + 301x4 - 280x3 + 2128x2 + 320x + 6672 $2^{18}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $181346.72701$
8.4.3628410392018944.3 x8 - 4x7 - 28x6 - 28x5 + 70x4 + 588x3 + 1764x2 + 1940x + 661 $2^{18}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) trivial $146393.854072$
8.4.3628410392018944.4 x8 - 4x7 - 14x6 + 56x5 + 84x4 - 28x3 - 112x2 - 16x + 50 $2^{18}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $51933.9162826$
8.0.12782719397154721.1 x8 - 3x7 - 56x6 + 28x5 + 1043x4 - 567x3 + 4704x2 + 46853x + 57555 $7^{12}\cdot 31^{4}$ $C_2^3:C_7$ (as 8T25) $[2, 2, 2]$ $20731.5393723$
8.8.12782719397154721.1 x8 - x7 - 42x6 + 77x5 + 420x4 - 854x3 - 987x2 + 1577x + 733 $7^{12}\cdot 31^{4}$ $C_2^3:C_7$ (as 8T25) trivial $942691.948946$
8.4.14513641568075776.1 x8 - 4x7 + 14x6 - 28x5 - 273x4 - 84x3 + 2534x2 + 4384x - 9381 $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $208750.585146$
8.0.14513641568075776.2 x8 - 4x7 + 28x6 - 56x5 + 252x4 - 280x3 + 952x2 - 464x + 1380 $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 12]$ $15171.4047761$
8.0.14513641568075776.3 x8 - 56x5 + 126x4 + 224x3 - 112x2 + 1048x + 1505 $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $32642.9044999$
8.4.14513641568075776.5 x8 - 28x6 - 84x5 + 210x4 + 5096x3 + 13552x2 + 6008x - 2002 $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $144495.61499$
8.0.14513641568075776.7 x8 - 4x7 - 56x5 + 490x4 - 1008x3 + 1400x2 - 3296x + 4616 $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $44578.5697838$
8.4.14513641568075776.11 x8 - 4x7 - 28x6 + 56x5 + 686x4 - 4256x3 + 14112x2 - 16672x + 4080 $2^{20}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2]$ $896141.00032$
8.0.470772960728745024.2 x8 - 2x7 + 28x6 - 13608x + 27216 $2^{6}\cdot 3^{12}\cdot 7^{12}$ $\PSL(2,7)$ (as 8T37) $[4]$ $747394.855325$
8.0.928873060356849664.4 x8 + 56x6 + 952x4 - 896x3 + 7392x2 + 2304x + 15120 $2^{26}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 4]$ $258306.421026$
8.4.928873060356849664.7 x8 - 56x6 - 112x5 + 350x4 + 3528x3 + 11592x2 + 16120x + 6727 $2^{26}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[4]$ $719098.828771$
8.4.928873060356849664.8 x8 - 28x6 - 224x5 - 1176x4 - 1064x3 - 6104x2 - 7920x + 8442 $2^{26}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 2]$ $1034710.48001$
8.0.928873060356849664.12 x8 - 28x6 - 112x5 + 1386x4 + 6272x3 + 18060x2 - 49520x + 426209 $2^{26}\cdot 7^{12}$ $C_2^3:\GL(3,2)$ (as 8T48) $[2, 4]$ $121607.01614$
8.0.3715492241427398656.1 x8 - 896x + 1568 $2^{28}\cdot 7^{12}$ $A_8$ (as 8T49) $[2, 2]$ $468980.925517$
8.2.650...376.1 x8 - 3528x2 - 6048x - 2646 $-\,2^{31}\cdot 3^{7}\cdot 7^{12}$ $S_8$ (as 8T50) trivial $683277868.793$
8.2.131...864.1 x8 - 56x5 - 1050x4 - 8400x3 - 35000x2 - 75000x - 65625 $-\,2^{29}\cdot 3^{11}\cdot 7^{12}$ $S_8$ (as 8T50) $[2]$ $1754817880.49$
8.2.186...216.1 x8 - 5824x - 5096 $-\,2^{31}\cdot 7^{12}\cdot 13^{7}$ $S_8$ (as 8T50) $[2, 2]$ $16760064929.9$
9.3.203...368.1 x9 - 3x8 + 756x2 - 2268x + 1764 $-\,2^{10}\cdot 3^{15}\cdot 7^{12}$ $S_9$ (as 9T34) trivial $38577167.6361$
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