Elliptic curves in class 128.5-c over \(\Q(\sqrt{17}) \)
Isogeny class 128.5-c contains
12 curves linked by isogenies of
degrees dividing 24.
| Curve label |
Weierstrass Coefficients |
| 128.5-c1
| \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -285 a - 443\) , \( -4041 a - 6307\bigr] \)
|
| 128.5-c2
| \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a + 4\) , \( a + 2\bigr] \)
|
| 128.5-c3
| \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 24 a - 41\) , \( -98 a + 129\bigr] \)
|
| 128.5-c4
| \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 20 a + 32\) , \( 0\bigr] \)
|
| 128.5-c5
| \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 9 a - 24\) , \( 15 a - 41\bigr] \)
|
| 128.5-c6
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2431 a - 3923\) , \( 73584 a + 115495\bigr] \)
|
| 128.5-c7
| \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -791 a - 1243\) , \( -16960 a - 26473\bigr] \)
|
| 128.5-c8
| \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 146 a - 374\) , \( 0\bigr] \)
|
| 128.5-c9
| \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 149 a - 404\) , \( 1359 a - 3561\bigr] \)
|
| 128.5-c10
| \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 24 a - 179\) , \( -493 a + 579\bigr] \)
|
| 128.5-c11
| \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 1656 a - 4244\) , \( -51666 a + 132346\bigr] \)
|
| 128.5-c12
| \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -296 a - 1139\) , \( -7277 a - 16189\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 24 & 8 & 3 & 6 & 8 & 4 & 12 & 12 & 2 & 24 & 4 \\
24 & 1 & 3 & 8 & 4 & 12 & 6 & 2 & 8 & 12 & 4 & 24 \\
8 & 3 & 1 & 24 & 12 & 4 & 2 & 6 & 24 & 4 & 12 & 8 \\
3 & 8 & 24 & 1 & 2 & 24 & 12 & 4 & 4 & 6 & 8 & 12 \\
6 & 4 & 12 & 2 & 1 & 12 & 6 & 2 & 2 & 3 & 4 & 6 \\
8 & 12 & 4 & 24 & 12 & 1 & 2 & 6 & 24 & 4 & 3 & 8 \\
4 & 6 & 2 & 12 & 6 & 2 & 1 & 3 & 12 & 2 & 6 & 4 \\
12 & 2 & 6 & 4 & 2 & 6 & 3 & 1 & 4 & 6 & 2 & 12 \\
12 & 8 & 24 & 4 & 2 & 24 & 12 & 4 & 1 & 6 & 8 & 3 \\
2 & 12 & 4 & 6 & 3 & 4 & 2 & 6 & 6 & 1 & 12 & 2 \\
24 & 4 & 12 & 8 & 4 & 3 & 6 & 2 & 8 & 12 & 1 & 24 \\
4 & 24 & 8 & 12 & 6 & 8 & 4 & 12 & 3 & 2 & 24 & 1
\end{array}\right)\)
