Isogeny class 17.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
Curve label |
Weierstrass Coefficients |
17.1-a1
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a + 1\) , \( -12 a^{3} - 23 a^{2} + 11 a + 20\) , \( -38 a^{3} - 68 a^{2} + 26 a + 39\bigr] \)
|
17.1-a2
| \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 2 a + 1\) , \( -a^{3} - 7 a^{2} - 4 a + 8\) , \( -4 a^{3} - 8 a^{2} + 2 a + 5\bigr] \)
|
17.1-a3
| \( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -8 a^{3} - 16 a^{2} + 6 a + 11\) , \( -23 a^{3} - 43 a^{2} + 14 a + 25\bigr] \)
|
17.1-a4
| \( \bigl[a^{2} + a - 2\) , \( a^{3} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 3 a^{3} + 3 a^{2} - 13 a - 14\) , \( -15 a^{3} - 14 a^{2} + 47 a + 39\bigr] \)
|
17.1-a5
| \( \bigl[a^{3} - 3 a\) , \( a + 1\) , \( 1\) , \( -3 a^{3} - 2 a^{2} + 6 a\) , \( 3 a^{2} + 3 a - 5\bigr] \)
|
17.1-a6
| \( \bigl[a\) , \( a^{2} + a - 1\) , \( a + 1\) , \( -14 a^{3} + 14 a^{2} + 52 a - 42\) , \( -43 a^{3} + 36 a^{2} + 150 a - 117\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 2 & 4 & 8 & 8 \\
4 & 1 & 2 & 4 & 2 & 2 \\
2 & 2 & 1 & 2 & 4 & 4 \\
4 & 4 & 2 & 1 & 8 & 8 \\
8 & 2 & 4 & 8 & 1 & 4 \\
8 & 2 & 4 & 8 & 4 & 1
\end{array}\right)\)