Isogeny class 64.1-b contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 64.1-b1
| \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{2} - a - 2\) , \( 0\) , \( -5 a^{3} - a^{2} + 19 a + 10\) , \( 2 a^{3} + 2 a^{2} - 7 a - 4\bigr] \)
|
| 64.1-b2
| \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{2} - a - 2\) , \( 0\) , \( -a^{3} - a^{2} - a\) , \( -2 a^{3} - 3 a^{2} + a + 1\bigr] \)
|
| 64.1-b3
| \( \bigl[a^{3} - 3 a\) , \( 1\) , \( 0\) , \( -2\) , \( -3\bigr] \)
|
| 64.1-b4
| \( \bigl[a^{3} - 3 a\) , \( 1\) , \( a^{3} - 3 a\) , \( -3\) , \( 0\bigr] \)
|
| 64.1-b5
| \( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 1\) , \( -16 a^{3} + 3 a^{2} + 63 a - 28\) , \( 19 a^{3} + 21 a^{2} - 146 a + 68\bigr] \)
|
| 64.1-b6
| \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 5 a - 1\) , \( a^{3} - 4 a + 1\) , \( -15 a^{3} + 5 a^{2} + 58 a - 31\) , \( -35 a^{3} - 17 a^{2} + 209 a - 99\bigr] \)
|
| 64.1-b7
| \( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a + 1\) , \( 14 a^{3} + 3 a^{2} - 59 a - 29\) , \( -16 a^{3} + 20 a^{2} + 117 a + 53\bigr] \)
|
| 64.1-b8
| \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 5 a - 1\) , \( 0\) , \( 14 a^{3} + 5 a^{2} - 61 a - 30\) , \( 30 a^{3} - 16 a^{2} - 177 a - 83\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 2 & 4 & 4 & 8 & 8 & 8 & 8 \\
2 & 1 & 2 & 2 & 4 & 4 & 4 & 4 \\
4 & 2 & 1 & 4 & 8 & 2 & 8 & 2 \\
4 & 2 & 4 & 1 & 2 & 8 & 2 & 8 \\
8 & 4 & 8 & 2 & 1 & 16 & 4 & 16 \\
8 & 4 & 2 & 8 & 16 & 1 & 16 & 4 \\
8 & 4 & 8 & 2 & 4 & 16 & 1 & 16 \\
8 & 4 & 2 & 8 & 16 & 4 & 16 & 1
\end{array}\right)\)
