Isogeny class 31.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 31.1-a1
| \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -427 a^{3} - 156 a^{2} + 1210 a - 328\) , \( 5301 a^{3} + 2573 a^{2} - 14446 a + 2048\bigr] \)
|
| 31.1-a2
| \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( 113 a^{3} + 114 a^{2} - 280 a - 98\) , \( -a^{3} - 75 a^{2} + 44 a + 78\bigr] \)
|
| 31.1-a3
| \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -37 a^{3} - 21 a^{2} + 105 a - 13\) , \( 2 a^{3} - 25 a^{2} - 17 a + 63\bigr] \)
|
| 31.1-a4
| \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -2 a^{3} - a^{2} + 5 a + 2\) , \( -2 a^{3} - 2 a^{2} + 5 a + 1\bigr] \)
|
| 31.1-a5
| \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -22 a^{3} - 21 a^{2} + 60 a + 12\) , \( -77 a^{3} - 67 a^{2} + 195 a + 43\bigr] \)
|
| 31.1-a6
| \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 1\) , \( -327 a^{3} - 341 a^{2} + 895 a + 197\) , \( -4716 a^{3} - 4369 a^{2} + 12267 a + 2711\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 2 & 8 & 4 & 8 \\
4 & 1 & 2 & 8 & 4 & 8 \\
2 & 2 & 1 & 4 & 2 & 4 \\
8 & 8 & 4 & 1 & 2 & 4 \\
4 & 4 & 2 & 2 & 1 & 2 \\
8 & 8 & 4 & 4 & 2 & 1
\end{array}\right)\)
