Isogeny class 31.1-b contains
6 curves linked by isogenies of
degrees dividing 8.
Curve label |
Weierstrass Coefficients |
31.1-b1
| \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( -80 a^{3} + 335 a^{2} + 315 a - 1284\) , \( -2177 a^{3} + 4753 a^{2} + 8378 a - 18117\bigr] \)
|
31.1-b2
| \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( -5 a^{3} + 20 a^{2} + 20 a - 79\) , \( -42 a^{3} + 85 a^{2} + 161 a - 317\bigr] \)
|
31.1-b3
| \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( -10 a^{3} + 25 a^{2} + 45 a - 74\) , \( 9 a^{3} + 101 a^{2} - 28 a - 357\bigr] \)
|
31.1-b4
| \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( 5 a^{3} - 20 a^{2} - 20 a - 9\) , \( -4 a^{3} + 99 a^{2} + 23 a - 5\bigr] \)
|
31.1-b5
| \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( -4\) , \( -a^{3} + 4 a^{2} + 4 a - 7\bigr] \)
|
31.1-b6
| \( \bigl[a^{2} - 2\) , \( -a^{2} + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 8 & 4 & 8 \\
2 & 1 & 2 & 4 & 2 & 4 \\
4 & 2 & 1 & 8 & 4 & 8 \\
8 & 4 & 8 & 1 & 2 & 4 \\
4 & 2 & 4 & 2 & 1 & 2 \\
8 & 4 & 8 & 4 & 2 & 1
\end{array}\right)\)