Elliptic curves in class 55.2-a over \(\Q(\sqrt{5}) \)
Isogeny class 55.2-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 55.2-a1
| \( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( -\phi\) , \( 0\bigr] \)
|
| 55.2-a2
| \( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( 4 \phi - 5\) , \( -2 \phi - 15\bigr] \)
|
| 55.2-a3
| \( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( 4 \phi - 30\) , \( -29 \phi + 37\bigr] \)
|
| 55.2-a4
| \( \bigl[1\) , \( \phi\) , \( 1\) , \( -54 \phi + 54\) , \( 374 \phi - 572\bigr] \)
|
| 55.2-a5
| \( \bigl[1\) , \( \phi\) , \( 1\) , \( 21 \phi - 46\) , \( 54 \phi - 112\bigr] \)
|
| 55.2-a6
| \( \bigl[\phi\) , \( -\phi + 1\) , \( \phi\) , \( -6 \phi - 5\) , \( 8 \phi + 5\bigr] \)
|
| 55.2-a7
| \( \bigl[1\) , \( \phi\) , \( 1\) , \( 16 \phi - 226\) , \( -1110 \phi + 576\bigr] \)
|
| 55.2-a8
| \( \bigl[1\) , \( \phi\) , \( 1\) , \( -9 \phi - 16\) , \( 6 \phi + 38\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\
3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\
4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\
12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\
6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\
2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\
12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\
4 & 12 & 4 & 3 & 6 & 2 & 12 & 1
\end{array}\right)\)
