Elliptic curves in class 81.1-a over \(\Q(\sqrt{5}) \)
Isogeny class 81.1-a contains
8 curves linked by isogenies of
degrees dividing 30.
| Curve label |
Weierstrass Coefficients |
| 81.1-a1
| \( \bigl[1\) , \( -1\) , \( \phi\) , \( -2 \phi\) , \( \phi\bigr] \)
|
| 81.1-a2
| \( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( -14 \phi - 2\) , \( -21 \phi - 6\bigr] \)
|
| 81.1-a3
| \( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( \phi - 2\) , \( -2 \phi + 1\bigr] \)
|
| 81.1-a4
| \( \bigl[1\) , \( -1\) , \( \phi\) , \( 13 \phi - 15\) , \( 20 \phi - 26\bigr] \)
|
| 81.1-a5
| \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( -13 \phi - 14\) , \( -20 \phi - 6\bigr] \)
|
| 81.1-a6
| \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi\) , \( -113 \phi - 125\) , \( 867 \phi + 384\bigr] \)
|
| 81.1-a7
| \( \bigl[\phi + 1\) , \( 1\) , \( 1\) , \( 13 \phi - 26\) , \( 32 \phi - 51\bigr] \)
|
| 81.1-a8
| \( \bigl[\phi + 1\) , \( 1\) , \( 0\) , \( 114 \phi - 237\) , \( -754 \phi + 1014\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 15 & 5 & 3 & 10 & 6 & 2 & 30 \\
15 & 1 & 3 & 5 & 6 & 10 & 30 & 2 \\
5 & 3 & 1 & 15 & 2 & 30 & 10 & 6 \\
3 & 5 & 15 & 1 & 30 & 2 & 6 & 10 \\
10 & 6 & 2 & 30 & 1 & 15 & 5 & 3 \\
6 & 10 & 30 & 2 & 15 & 1 & 3 & 5 \\
2 & 30 & 10 & 6 & 5 & 3 & 1 & 15 \\
30 & 2 & 6 & 10 & 3 & 5 & 15 & 1
\end{array}\right)\)
