Elliptic curves in class 31.1-a over 4.4.725.1
Isogeny class 31.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 31.1-a1
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( 396 a^{3} - 114 a^{2} - 1262 a - 535\) , \( 5675 a^{3} - 1590 a^{2} - 18077 a - 7642\bigr] \)
|
| 31.1-a2
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( -24 a^{3} + 26 a^{2} + 68 a - 60\) , \( 61 a^{3} - 64 a^{2} - 197 a + 150\bigr] \)
|
| 31.1-a3
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( 26 a^{3} - 24 a^{2} - 72 a - 30\) , \( 81 a^{3} - 76 a^{2} - 269 a - 102\bigr] \)
|
| 31.1-a4
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( a^{3} + a^{2} - 2 a - 5\) , \( a^{3} - 5 a - 2\bigr] \)
|
| 31.1-a5
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( a^{3} + a^{2} - 2 a\) , \( a^{3} - a\bigr] \)
|
| 31.1-a6
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - a^{2} - a + 1\) , \( 1\) , \( 56 a^{3} - 334 a^{2} - 2 a + 75\) , \( 107 a^{3} - 3446 a^{2} + 603 a + 1078\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 2 & 4 & 8 & 4 \\
8 & 1 & 4 & 2 & 4 & 8 \\
2 & 4 & 1 & 2 & 4 & 2 \\
4 & 2 & 2 & 1 & 2 & 4 \\
8 & 4 & 4 & 2 & 1 & 8 \\
4 & 8 & 2 & 4 & 8 & 1
\end{array}\right)\)
