Elliptic curves in class 45.1-a over \(\Q(\sqrt{65}) \)
Isogeny class 45.1-a contains
8 curves linked by isogenies of
degrees dividing 16.
Curve label |
Weierstrass Coefficients |
45.1-a1
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( -986 a - 3512\) , \( -67741 a - 239296\bigr] \)
|
45.1-a2
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( 4 a + 8\) , \( 19 a + 64\bigr] \)
|
45.1-a3
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( 319 a + 1128\) , \( -2137 a - 7552\bigr] \)
|
45.1-a4
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( -86 a - 312\) , \( -751 a - 2656\bigr] \)
|
45.1-a5
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( -41 a - 152\) , \( 173 a + 608\bigr] \)
|
45.1-a6
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( -1211 a - 4312\) , \( -50801 a - 179456\bigr] \)
|
45.1-a7
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( -716 a - 2552\) , \( 18653 a + 65888\bigr] \)
|
45.1-a8
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( -19436 a - 69112\) , \( -3044561 a - 10754816\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\
16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\
8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\
4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\
8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\
2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\
16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\
4 & 16 & 8 & 4 & 8 & 2 & 16 & 1
\end{array}\right)\)