Elliptic curves in class 576.6-n over \(\Q(\sqrt{17}) \)
Isogeny class 576.6-n contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 576.6-n1
| \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -19 a - 36\) , \( 66 a + 110\bigr] \)
|
| 576.6-n2
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 294 a + 455\) , \( -43002 a - 67154\bigr] \)
|
| 576.6-n3
| \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 28 a + 52\) , \( 175 a + 261\bigr] \)
|
| 576.6-n4
| \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -7 a - 13\) , \( 0\bigr] \)
|
| 576.6-n5
| \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 271 a - 686\) , \( 3406 a - 8718\bigr] \)
|
| 576.6-n6
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 39 a - 110\) , \( -192 a + 492\bigr] \)
|
| 576.6-n7
| \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -23 a - 40\) , \( -94 a - 160\bigr] \)
|
| 576.6-n8
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -36 a + 25\) , \( -702 a + 1986\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\
16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\
8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\
4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\
8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\
2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\
16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\
4 & 16 & 8 & 4 & 8 & 2 & 16 & 1
\end{array}\right)\)
