Elliptic curves in class 576.6-e over \(\Q(\sqrt{17}) \)
Isogeny class 576.6-e contains
8 curves linked by isogenies of
degrees dividing 16.
Curve label |
Weierstrass Coefficients |
576.6-e1
| \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 100 a - 256\) , \( -813 a + 2081\bigr] \)
|
576.6-e2
| \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 71 a - 156\) , \( 446 a - 779\bigr] \)
|
576.6-e3
| \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -122 a + 308\) , \( 1028 a - 2637\bigr] \)
|
576.6-e4
| \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 43 a - 117\) , \( 188 a - 485\bigr] \)
|
576.6-e5
| \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -4 a - 21\) , \( 11 a + 4\bigr] \)
|
576.6-e6
| \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -61 a - 98\) , \( -437 a - 681\bigr] \)
|
576.6-e7
| \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 99 a - 258\) , \( 1083 a - 2777\bigr] \)
|
576.6-e8
| \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -976 a - 1523\) , \( -24827 a - 38763\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\
16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\
8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\
4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\
8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\
2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\
16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\
4 & 16 & 8 & 4 & 8 & 2 & 16 & 1
\end{array}\right)\)