Elliptic curves in class 55.1-a over \(\Q(\sqrt{5}) \)
Isogeny class 55.1-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 55.1-a1
| \( \bigl[1\) , \( -\phi + 1\) , \( 1\) , \( 9 \phi - 25\) , \( -6 \phi + 44\bigr] \)
|
| 55.1-a2
| \( \bigl[1\) , \( -\phi + 1\) , \( 1\) , \( 54 \phi\) , \( -374 \phi - 198\bigr] \)
|
| 55.1-a3
| \( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( -\phi - 1\) , \( -\phi\bigr] \)
|
| 55.1-a4
| \( \bigl[1\) , \( -\phi + 1\) , \( 1\) , \( -21 \phi - 25\) , \( -54 \phi - 58\bigr] \)
|
| 55.1-a5
| \( \bigl[1\) , \( -\phi + 1\) , \( 1\) , \( -16 \phi - 210\) , \( 1110 \phi - 534\bigr] \)
|
| 55.1-a6
| \( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( 4 \phi - 11\) , \( -9 \phi + 13\bigr] \)
|
| 55.1-a7
| \( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( -6 \phi - 1\) , \( \phi - 17\bigr] \)
|
| 55.1-a8
| \( \bigl[\phi + 1\) , \( 0\) , \( \phi + 1\) , \( -6 \phi - 26\) , \( 28 \phi + 8\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 6 & 12 & 2 & 12 & 4 \\
3 & 1 & 12 & 2 & 4 & 6 & 4 & 12 \\
4 & 12 & 1 & 6 & 12 & 2 & 3 & 4 \\
6 & 2 & 6 & 1 & 2 & 3 & 2 & 6 \\
12 & 4 & 12 & 2 & 1 & 6 & 4 & 3 \\
2 & 6 & 2 & 3 & 6 & 1 & 6 & 2 \\
12 & 4 & 3 & 2 & 4 & 6 & 1 & 12 \\
4 & 12 & 4 & 6 & 3 & 2 & 12 & 1
\end{array}\right)\)
