Elliptic curves in class 576.7-e over \(\Q(\sqrt{17}) \)
Isogeny class 576.7-e contains
8 curves linked by isogenies of
degrees dividing 16.
Curve label |
Weierstrass Coefficients |
576.7-e1
| \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -101 a - 157\) , \( -1084 a - 1693\bigr] \)
|
576.7-e2
| \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 974 a - 2497\) , \( 24826 a - 63589\bigr] \)
|
576.7-e3
| \( \bigl[a\) , \( 0\) , \( a\) , \( 120 a + 188\) , \( -1029 a - 1608\bigr] \)
|
576.7-e4
| \( \bigl[a\) , \( 0\) , \( a\) , \( -45 a - 72\) , \( -189 a - 296\bigr] \)
|
576.7-e5
| \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 59 a - 157\) , \( 436 a - 1117\bigr] \)
|
576.7-e6
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a - 29\) , \( -34 a + 35\bigr] \)
|
576.7-e7
| \( \bigl[a\) , \( -a\) , \( 0\) , \( -100 a - 156\) , \( 813 a + 1268\bigr] \)
|
576.7-e8
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( -68 a - 89\) , \( -604 a - 613\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\
16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\
8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\
4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\
8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\
2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\
16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\
4 & 16 & 8 & 4 & 8 & 2 & 16 & 1
\end{array}\right)\)