Isogeny class 31.3-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 31.3-a1
| \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 495 a^{3} + 69 a^{2} - 1642 a - 353\) , \( -7129 a^{3} - 1543 a^{2} + 24030 a + 5034\bigr] \)
|
| 31.3-a2
| \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 410 a^{3} + 84 a^{2} - 1572 a - 328\) , \( 6096 a^{3} + 1625 a^{2} - 22572 a - 4736\bigr] \)
|
| 31.3-a3
| \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 40 a^{3} + 4 a^{2} - 142 a - 28\) , \( -32 a^{3} - 5 a^{2} + 76 a + 16\bigr] \)
|
| 31.3-a4
| \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 25 a^{3} + 4 a^{2} - 97 a - 18\) , \( 82 a^{3} + 20 a^{2} - 308 a - 64\bigr] \)
|
| 31.3-a5
| \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -a^{2} - 2 a + 2\) , \( 2 a^{3} - 8 a - 1\bigr] \)
|
| 31.3-a6
| \( \bigl[a^{3} - 2 a\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -175 a^{3} - 61 a^{2} + 638 a + 137\) , \( 89 a^{3} + 13 a^{2} - 402 a - 82\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 2 & 4 & 8 & 4 \\
8 & 1 & 4 & 2 & 4 & 8 \\
2 & 4 & 1 & 2 & 4 & 2 \\
4 & 2 & 2 & 1 & 2 & 4 \\
8 & 4 & 4 & 2 & 1 & 8 \\
4 & 8 & 2 & 4 & 8 & 1
\end{array}\right)\)
