Elliptic curves in class 81.1-a over \(\Q(\sqrt{13}) \)
Isogeny class 81.1-a contains
12 curves linked by isogenies of
degrees dividing 24.
Curve label |
Weierstrass Coefficients |
81.1-a1
| \( \bigl[a\) , \( -a\) , \( a + 1\) , \( -4 a + 3\) , \( -4 a + 5\bigr] \)
|
81.1-a2
| \( \bigl[a + 1\) , \( -1\) , \( a\) , \( -43 a - 360\) , \( 1020 a + 3386\bigr] \)
|
81.1-a3
| \( \bigl[a\) , \( -a\) , \( a + 1\) , \( 2381 a - 5352\) , \( -81841 a + 187736\bigr] \)
|
81.1-a4
| \( \bigl[a + 1\) , \( -1\) , \( a\) , \( 2 a\) , \( 3 a + 2\bigr] \)
|
81.1-a5
| \( \bigl[a + 1\) , \( -1\) , \( a\) , \( 2 a - 45\) , \( 39 a - 61\bigr] \)
|
81.1-a6
| \( \bigl[a\) , \( -a\) , \( a + 1\) , \( 131 a - 357\) , \( -1237 a + 2759\bigr] \)
|
81.1-a7
| \( \bigl[a\) , \( -a\) , \( a + 1\) , \( 41 a - 402\) , \( -1021 a + 4406\bigr] \)
|
81.1-a8
| \( \bigl[a + 1\) , \( -1\) , \( a\) , \( 137 a - 585\) , \( 1686 a - 5677\bigr] \)
|
81.1-a9
| \( \bigl[a + 1\) , \( -1\) , \( a\) , \( -133 a - 225\) , \( 1236 a + 1523\bigr] \)
|
81.1-a10
| \( \bigl[a\) , \( -a\) , \( a + 1\) , \( -4 a - 42\) , \( -40 a - 22\bigr] \)
|
81.1-a11
| \( \bigl[a + 1\) , \( -1\) , \( a\) , \( -2383 a - 2970\) , \( 81840 a + 105896\bigr] \)
|
81.1-a12
| \( \bigl[a\) , \( -a\) , \( a + 1\) , \( -139 a - 447\) , \( -1687 a - 3991\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 24 & 8 & 3 & 6 & 4 & 8 & 12 & 12 & 2 & 24 & 4 \\
24 & 1 & 3 & 8 & 4 & 6 & 12 & 8 & 2 & 12 & 4 & 24 \\
8 & 3 & 1 & 24 & 12 & 2 & 4 & 24 & 6 & 4 & 12 & 8 \\
3 & 8 & 24 & 1 & 2 & 12 & 24 & 4 & 4 & 6 & 8 & 12 \\
6 & 4 & 12 & 2 & 1 & 6 & 12 & 2 & 2 & 3 & 4 & 6 \\
4 & 6 & 2 & 12 & 6 & 1 & 2 & 12 & 3 & 2 & 6 & 4 \\
8 & 12 & 4 & 24 & 12 & 2 & 1 & 24 & 6 & 4 & 3 & 8 \\
12 & 8 & 24 & 4 & 2 & 12 & 24 & 1 & 4 & 6 & 8 & 3 \\
12 & 2 & 6 & 4 & 2 & 3 & 6 & 4 & 1 & 6 & 2 & 12 \\
2 & 12 & 4 & 6 & 3 & 2 & 4 & 6 & 6 & 1 & 12 & 2 \\
24 & 4 & 12 & 8 & 4 & 6 & 3 & 8 & 2 & 12 & 1 & 24 \\
4 & 24 & 8 & 12 & 6 & 4 & 8 & 3 & 12 & 2 & 24 & 1
\end{array}\right)\)