Isogeny class 17.2-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 17.2-a1
| \( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -30 a^{2} + 43 a + 21\) , \( 103 a^{2} - 160 a - 66\bigr] \)
|
| 17.2-a2
| \( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -455 a^{2} + 738 a + 216\) , \( 7473 a^{2} - 11274 a - 5210\bigr] \)
|
| 17.2-a3
| \( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -475 a^{2} + 733 a + 296\) , \( 7691 a^{2} - 11788 a - 5014\bigr] \)
|
| 17.2-a4
| \( \bigl[a^{2} - 1\) , \( -a + 1\) , \( a^{2} + a - 2\) , \( -7615 a^{2} + 11768 a + 4776\) , \( 514961 a^{2} - 789514 a - 335090\bigr] \)
|
| 17.2-a5
| \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -64 a^{2} - 35 a - 5\) , \( -218 a^{2} - 740 a - 231\bigr] \)
|
| 17.2-a6
| \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -4 a^{2}\) , \( -7 a^{2} - 13 a - 4\bigr] \)
|
| 17.2-a7
| \( \bigl[a\) , \( a + 1\) , \( 0\) , \( a^{2}\) , \( 0\bigr] \)
|
| 17.2-a8
| \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -24 a^{2} + 35 a + 5\) , \( -104 a^{2} + 142 a + 47\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 4 & 2 & 4 & 12 & 6 & 3 & 12 \\
4 & 1 & 2 & 4 & 12 & 6 & 12 & 3 \\
2 & 2 & 1 & 2 & 6 & 3 & 6 & 6 \\
4 & 4 & 2 & 1 & 3 & 6 & 12 & 12 \\
12 & 12 & 6 & 3 & 1 & 2 & 4 & 4 \\
6 & 6 & 3 & 6 & 2 & 1 & 2 & 2 \\
3 & 12 & 6 & 12 & 4 & 2 & 1 & 4 \\
12 & 3 & 6 & 12 & 4 & 2 & 4 & 1
\end{array}\right)\)
