Elliptic curves in class 128.5-b over \(\Q(\sqrt{17}) \)
Isogeny class 128.5-b contains
12 curves linked by isogenies of
degrees dividing 24.
| Curve label |
Weierstrass Coefficients |
| 128.5-b1
| \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -23 a + 42\) , \( -329 a + 864\bigr] \)
|
| 128.5-b2
| \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -89 a + 228\) , \( -57 a + 146\bigr] \)
|
| 128.5-b3
| \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 274 a + 429\) , \( 18518 a + 28917\bigr] \)
|
| 128.5-b4
| \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 2 a - 3\) , \( 14 a - 35\bigr] \)
|
| 128.5-b5
| \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -33 a - 52\) , \( 13 a + 20\bigr] \)
|
| 128.5-b6
| \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 1996 a - 5262\) , \( -72821 a + 185664\bigr] \)
|
| 128.5-b7
| \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 116 a - 342\) , \( -1173 a + 3040\bigr] \)
|
| 128.5-b8
| \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( a - 7\) , \( -7 a - 6\bigr] \)
|
| 128.5-b9
| \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -373 a - 592\) , \( 5721 a + 8920\bigr] \)
|
| 128.5-b10
| \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -1898 a - 2967\) , \( 64912 a + 101365\bigr] \)
|
| 128.5-b11
| \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -9 a - 117\) , \( -339 a - 74\bigr] \)
|
| 128.5-b12
| \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 10858 a - 27827\) , \( 698508 a - 1789259\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 24 & 8 & 3 & 6 & 8 & 4 & 12 & 12 & 2 & 24 & 4 \\
24 & 1 & 3 & 8 & 4 & 12 & 6 & 2 & 8 & 12 & 4 & 24 \\
8 & 3 & 1 & 24 & 12 & 4 & 2 & 6 & 24 & 4 & 12 & 8 \\
3 & 8 & 24 & 1 & 2 & 24 & 12 & 4 & 4 & 6 & 8 & 12 \\
6 & 4 & 12 & 2 & 1 & 12 & 6 & 2 & 2 & 3 & 4 & 6 \\
8 & 12 & 4 & 24 & 12 & 1 & 2 & 6 & 24 & 4 & 3 & 8 \\
4 & 6 & 2 & 12 & 6 & 2 & 1 & 3 & 12 & 2 & 6 & 4 \\
12 & 2 & 6 & 4 & 2 & 6 & 3 & 1 & 4 & 6 & 2 & 12 \\
12 & 8 & 24 & 4 & 2 & 24 & 12 & 4 & 1 & 6 & 8 & 3 \\
2 & 12 & 4 & 6 & 3 & 4 & 2 & 6 & 6 & 1 & 12 & 2 \\
24 & 4 & 12 & 8 & 4 & 3 & 6 & 2 & 8 & 12 & 1 & 24 \\
4 & 24 & 8 & 12 & 6 & 8 & 4 & 12 & 3 & 2 & 24 & 1
\end{array}\right)\)
