| Locus | Group ID | Signature |
Generators | Comments and Favorite Equations | Additional files |
| 1 | (192,181) | (2,3,8) |
\( \left[\begin{array}{rrrrr}
0 & 0 & \frac{1}{2}(i+1) & 0 & 0 \\
0 & -1 & 0 & 0 & 0\\
1-i & 0 & 0 & 0 & 0\\
0 & 0 & 0 & -\frac{1}{\sqrt{2}} & -\frac{i}{\sqrt{2}}\\
0 & 0 & 0 & \frac{i}{\sqrt{2}} & \frac{1}{\sqrt{2}}
\end{array} \right], \quad \left[\begin{array}{rrrrr}
0 & \zeta_8^{-1} & 0 & 0 & 0 \\
0 & 0 & -\frac{1}{\sqrt{2}} & 0 & 0\\
-1-i & 0 & 0 & 0 & 0\\
0 & 0 & 0 & \frac{1}{2}(i-1) & -\frac{1}{2}(i+1)\\
0 & 0 & 0 & -\frac{1}{2}(i-1) & -\frac{1}{2}(i+1)
\end{array} \right]
\)
|
| Wiman, 1895 |
| \( x_0^2+x_3^2+x_4^2\) |
| \( x_1^2+x_3^2-x_4^2\) |
| \( x_2^2+x_3 x_4\) |
|
|
| 2 | (160,234) | (2,4,5) |
\( \left[\begin{array}{rrrrr}
0 & 0 & 0 & -1 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
-1 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & -1
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & -1 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & -1 & 0 & 0 \\
0 & 1 & 0 & 0 & 0
\end{array} \right]
\) |
| Wiman, 1895 |
| \( x_0^2+x_1^2+x_2^2+x_3^2+x_4^2,\) |
| \( x_0^2+\zeta_5 x_1^2+\zeta_5^2x_2^2+\zeta_5^3 x_3^2+\zeta_5^4 x_4^2, \) |
| \( \zeta_5^4 x_0^2+\zeta_5^3 x_1^2+\zeta_5^2 x_2^2+\zeta_5 x_3^2+x_4^2\) |
| Genus-5-160-234.htm |
| 3 | (120,35) | (2,3,10) |
| (1, 4)(3, 5)(6, 7), |
| (2, 4, 5) |
|
| Hyperelliptic |
| \( y^2 = x^{11}-11 x^6-x\) |
| Genus-5-120-35.txt |
| 4 | (96,195) | (96,195) |
\( \left[\begin{array}{rrrrr}
0 & 0 & -1 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 \\
-1 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & \zeta_3 \\
0 & 0 & 0 & \zeta_3^2 & 0
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & 0 & -1 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 1 \\
0 & 0 & 0 & -1 & 0
\end{array} \right]
\)
|
| Wiman, 1895 |
| \( x_0^2 + x_3^2 + x_4^2,\) |
| \( x_1^2+\zeta_3 x_3^2+\zeta_3^2 x_4^2,\) |
| \( x_2^2+\zeta_3^2 x_3^2+\zeta_3 x_4^2\) |
| Genus-5-96-195.htm |
| 5 | (64,32) | (2,4,8) |
\( \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & -1 & 0 & 0 \\
0 & 0 & 0 & -1 & 0 \\
0 & 0 & 0 & 0 & -1
\end{array} \right], \quad \left[\begin{array}{rrrrr}
0 & 0 & 0 & -i& 0 \\
i & 0 & 0 & 0 & 0 \\
0 & -i & 0 & 0 & 0 \\
0 & 0 & i & 0 & 0 \\
0 & 0 & 0 & 0 & i
\end{array} \right]
\)
|
| Wiman, 1895 |
| \( x_0^2+x_1^2+x_2^2+x_3^2+x_4^2,\) |
| \( x_0^2+i x_1^2-x_2^2-i x_3^2,\) |
| \( x_0^2-x_1^2+x_2^2-x_3^2\) |
| Genus-5-64-32.htm |
| 6 | (48,14) | (2,4,12) |
| \((1, 20)(2, 17)(3, 24)(4, 12)(5, 11)(6, 16)(7, 23)(9, 19)(10, 18)(13, 22)\) |
| \((1, 6, 9, 7)(2, 3, 13, 4)(5, 16, 18, 23)(8, 19, 21, 20)(10, 22, 11, 17)(12, 14, 24, 15)\) |
|
| Hyperelliptic |
| \( y^2 = x^{12}-1\) |
| Genus-5-48-14.txt |
| 7 | (48,30) | (3,4,4) |
| \((1, 11, 4)(2, 14, 7)(3, 15, 9)(6, 16, 12) \) |
| \( (1, 6, 3, 2)(4, 12, 9, 7)(5, 16, 10, 14)(8, 11, 13, 15) \) |
|
| Hyperelliptic |
| \( y^2 = x^{12}-33x^8-33x^4+1\) |
|
Genus-5-48-30.txt |
| 8 | (40,5) | (2,4,20) |
| \( (4, 8)(6, 11)(7, 13)(9, 15)(10, 16)(12, 18)(14, 19)(17, 20)\) |
| \( (1, 12, 3, 17)(2, 14, 5, 9)(4, 6, 7, 10)(8, 18, 13, 20)(11, 19, 16, 15) \) |
| Hyperelliptic | Genus-5-40-5.txt |
| 9 | (30,2) |
(2,6,15) |
\( \left[\begin{array}{rrrrr}
0 & \zeta_{15}^{12} & 0 & 0 & 0 \\
\zeta_{15}^{3} & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & -\zeta_{15}^{9} \\
0 & 0 & 0 & -1 & 0 \\
0 & 0 & -\zeta_{15}^{6} & 0 & 0
\end{array} \right], \quad \left[\begin{array}{rrrrr}
0 & \zeta_{15}^{11} & 0 & 0 & 0 \\
\zeta_{15}^{14} & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & -\zeta_{15}^{7} \\
0 & 0 & 0 & -\zeta_{15}^{10} & 0 \\
0 & 0 & -\zeta_{15}^{13} & 0 & 0
\end{array} \right]
\)
|
| Cyclic trigonal \( y^3 = (x^5-1)x^2 \) |
| Canonical ideal: \( x_0 x_3-x_1 x_2\) |
| \( x_0 x_4-x_1 x_3 \) |
| \( x_2 x_4-x_3^2\) |
| \(x_0^2 x_1-x_3 x_4^2+x_2^3 \) |
| \( x_0 x_1^2-x_4^3+x_2^2 x_3\) |
| Genus-5-30-2.htm |
| 10 | (22,2) | (2,11,22) |
| \( (1, 2)(3, 5)(4, 6)(7, 9)(8, 10)(11, 13)(12, 14)(15, 17)(16, 18)(19, 21)(20, 22)\) |
| \( (1, 8, 16, 19, 11, 3, 4, 12, 20, 15, 7)(2, 10, 18, 21, 13, 5, 6, 14, 22, 17, 9)\) |
|
| Hyperelliptic |
| \( y^2 = x^{11}-1\) |
| Genus-5-22-2.txt |
| Locus | Group ID | Signature |
Generators | Comments and Favorite Equations | Additional files |
| 11 | (48,48) | (2,2,2,3) |
\( \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 \\
0 & 0 & -1 & 0 & 0 \\
0 & 0 & 0 & -1 & 0 \\
0 & 0 & -1 & 1 & 1
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1 & -1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & -1\\
0 & 0 & 1 & -1 & -1 \\
0 & 0 & -1 & 0 & 0
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 0 \\
0 & 0 & -1 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & -1 & -1
\end{array} \right]
\)
|
| \( x_0^2 - x_0 x_1 + x_1^2+x_2^2 + x_2 x_4 + x_3^2 - x_3 x_4 + x_4^2,\) |
| \( x_0^2 - x_1^2+c_4 (x_2^2 - 2 x_2 x_3 + 2 x_2 x_4 + x_3^2 - 2 x_3 x_4),\) |
| \( x_0 x_1 - 1/2 x_1^2 + c_4 (-2 x_2 x_3 + x_2 x_4 - x_3 x_4 + 1/2 x_4^2)\) |
| Genus-5-48-48.htm |
| 12 | (32,43) | (2,2,2,4) |
\( \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & 0 & i & 0 & 0 \\
0 & -i & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & -i \\
0 & 0 & 0 & i & 0
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & -i \\
0 & 0 & 0 & -1 & 0 \\
0 & 0 & -1 & 0 & 0 \\
0 & i & 0 & 0 & 0
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & 0 & -i & 0 & 0 \\
0 & i & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & -i \\
0 & 0 & 0 & i & 0
\end{array} \right]
\)
|
| \( x_0^2+x_1 x_2 - i x_3 x_4,\) |
| \( x_1^2+i x_3^2+c_4 (x_2^2-i x_4^2),\) |
| \( i x_2^2-x_4^2+c_4 (i x_1^2+x_3^2)\) |
| Genus-5-32-43.htm |
| 13 | (32,28) | (2,2,2,4) |
\( \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 \\
0 & 0 & -1 & 0 & 0 \\
0 & 0 & 0 & 0 & -i \\
0 & 0 & 0 & i & 0
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 0 & -1 \\
0 & 0 & 0 & -1 & 0
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & 0 & -1 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 \\
0 & 0 & 0 & -1 & 0 \\
0 & 0 & 0 & 0 & 1
\end{array} \right]
\)
|
| \( x_0^2+x_1^2 + x_2^2,\) |
| \( x_1 x_2+x_3^2 - x_4^2,\) |
| \( x_1^2 - x_2^2+c_6 (x_3 x_4)\) |
| Genus-5-32-28.htm |
| 14 | (32,27) | (2,2,2,4) |
\( \left[\begin{array}{rrrrr}
-1& 0 & 0 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 \\
0 & 0 & -1 & 0 & 0 \\
0 & 0 & 0 & 0 & -1 \\
0 & 0 & 0 & -1 & 0
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & 0 & -1 & 0 & 0 \\
0 & -1 & 0 & 0 & 0 \\
0 & 0 & 0 & -1 & 0 \\
0 & 0 & 0 & 0 & -1
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1 & 0 & 0 & 0 & 0 \\
0 & 0 & -i & 0 & 0 \\
0 & i & 0 & 0 & 0 \\
0 & 0 & 0 & -1 & 0 \\
0 & 0 & 0 & 0 & 1
\end{array} \right]
\)
|
| \( x_0^2+x_3^2 + x_4^2,\) |
| \( x_1 x_2+ x_3^2 + x_4^2,\) |
| \( x_1^2 + x_2^2+c_8 x_3 x_4\) |
| Genus-5-32-27.htm |
| 15 | (24,14) | (2,2,2,6) |
|
| \( (1, 4)(2, 6)(3, 7)(5, 9)\) |
|
| \( (1, 11)(2, 12)(3, 8)(4, 7)(5, 10)(6, 9)\) |
|
| \( (1, 2)(3, 5)(4, 6)(7, 9)(8, 10)(11, 12)\) |
|
| Hyperelliptic |
| \( y^2 = (x^6-t^6)(x^6-t^{-6})\) |
| Genus-5-24-14.txt |
| 16 | (24,8) | (2,2,2,6) |
\( \left[\begin{array}{rrrrr}
-1& 0 & 0 & 0 & 0 \\
0& -1 & 0 & 0 & 0 \\
0& 0 & -1 & 0 & 0 \\
0& 0 & 0 & -1 & 0 \\
0& 0 & 0 & 0 & 1
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1& 0 & 0 & 0 & 0 \\
0& 0 & -1 & 0 & 0 \\
0& -1 & 0 & 0 & 0 \\
0& 0 & 0 & 0 & \zeta_6-1 \\
0& 0 & 0 & -\zeta_6 & 0
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1& 0 & 0 & 0 & 0 \\
0& 1 & 0 & 0 & 0 \\
0& 1 & -1 & 0 & 0 \\
0& 0 & 0 & 0 & \zeta_6 \\
0& 0 & 0 & -\zeta_6+1 & 0
\end{array} \right]
\)
|
| \( x_0^2 + x_1^2 + x_1 x_2 + x_2^2,\) |
| \( x_0 x_1+c_4 (x_1^2 - 2 x_1 x_2 - 2 x_2^2)+x_3^2 + x_4^2,\) |
| \( x_0 x_2+c_4 (-2 x_1^2 - 2 x_1 x_2 + x_2^2)-\zeta_6 x_3^2 + (\zeta_6 - 1)x_4^2\) |
| Genus-5-24-8.htm |
| 17 | (24,13) | (2,2,3,3) |
\( \left[\begin{array}{rrrrr}
-1& 0 & 0 & 0 & 0 \\
0& -1 & 0 & 0 & 0 \\
0& 0 & 1 & 0 & 0 \\
0& 0 & 0 & -1 & 0 \\
0& 0 & 0 & 0 & 0-1
\end{array} \right], \quad \left[\begin{array}{rrrrr}
-1& 0 & 0 & 0 & 0 \\
0& -1 & 0 & 0 & 0 \\
0& 0 & 1 & 0 & 0 \\
0& 0 & 0 & -1 & 0 \\
0& 0 & 0 & 0 & -1
\end{array} \right], \quad \left[\begin{array}{rrrrr}
\zeta_6-1& 0 & 0 & 0 & 0 \\
0& -\zeta_6 & 0 & 0 & 0 \\
0& 0 & 0 & -1 & 0 \\
0& 0 & 0 & 0 & 1 \\
0& 0 & -1 & 0 & 0
\end{array} \right]
\)
|
| \( x_0 x_1 + x_2^2 + x_3^2 + x_4^2,\) |
| \( x_1^2 + x_2^2 + (\zeta_6 - 1) x_3^2 - \zeta_6 x_4^2,\) |
| \(x_0^2 + c_6 (x_2^2 - \zeta_6 x_3^2 + (\zeta_6-1) x_4^2) \) |
| Genus-5-24-13.htm |
| 18 | (20,4) | (2,2,2,10) |
| \( (1, 2)(3, 4)(5, 7)(6, 8)(9, 10)\) |
| \( (1, 8)(2, 6)(3, 4)(5, 10)(7, 9)\) |
| \( (1, 10)(2, 9)(3, 8)(4, 6)(5, 7)\) |
|
| Hyperelliptic |
| \( y^2 = x(x^5-t^5)(x^5-t^{-5}) \) |
| Genus-5-20-4.txt |
