Elliptic curves in class 32.3-a over \(\Q(\sqrt{17}) \)
Isogeny class 32.3-a contains
12 curves linked by isogenies of
degrees dividing 24.
| Curve label |
Weierstrass Coefficients |
| 32.3-a1
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -60 a + 146\) , \( 1782 a - 4567\bigr] \)
|
| 32.3-a2
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a - 6\) , \( -16 a - 25\bigr] \)
|
| 32.3-a3
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 21 a + 29\) , \( 404 a + 627\bigr] \)
|
| 32.3-a4
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 5 a - 19\) , \( -68 a + 171\bigr] \)
|
| 32.3-a5
| \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -2\) , \( -4 a - 5\bigr] \)
|
| 32.3-a6
| \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 6440 a - 16514\) , \( 410032 a - 1050341\bigr] \)
|
| 32.3-a7
| \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 400 a - 1034\) , \( 6672 a - 17093\bigr] \)
|
| 32.3-a8
| \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 5 a - 19\) , \( 6 a - 19\bigr] \)
|
| 32.3-a9
| \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -20 a - 62\) , \( 44 a + 139\bigr] \)
|
| 32.3-a10
| \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -145 a - 237\) , \( 1100 a + 1707\bigr] \)
|
| 32.3-a11
| \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 75 a - 209\) , \( 618 a - 1607\bigr] \)
|
| 32.3-a12
| \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -2385 a - 3757\) , \( 86220 a + 134699\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 24 & 8 & 3 & 6 & 8 & 4 & 12 & 12 & 2 & 24 & 4 \\
24 & 1 & 3 & 8 & 4 & 12 & 6 & 2 & 8 & 12 & 4 & 24 \\
8 & 3 & 1 & 24 & 12 & 4 & 2 & 6 & 24 & 4 & 12 & 8 \\
3 & 8 & 24 & 1 & 2 & 24 & 12 & 4 & 4 & 6 & 8 & 12 \\
6 & 4 & 12 & 2 & 1 & 12 & 6 & 2 & 2 & 3 & 4 & 6 \\
8 & 12 & 4 & 24 & 12 & 1 & 2 & 6 & 24 & 4 & 3 & 8 \\
4 & 6 & 2 & 12 & 6 & 2 & 1 & 3 & 12 & 2 & 6 & 4 \\
12 & 2 & 6 & 4 & 2 & 6 & 3 & 1 & 4 & 6 & 2 & 12 \\
12 & 8 & 24 & 4 & 2 & 24 & 12 & 4 & 1 & 6 & 8 & 3 \\
2 & 12 & 4 & 6 & 3 & 4 & 2 & 6 & 6 & 1 & 12 & 2 \\
24 & 4 & 12 & 8 & 4 & 3 & 6 & 2 & 8 & 12 & 1 & 24 \\
4 & 24 & 8 & 12 & 6 & 8 & 4 & 12 & 3 & 2 & 24 & 1
\end{array}\right)\)
