Elliptic curves in class 4455.2-a over \(\Q(\sqrt{5}) \)
Isogeny class 4455.2-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 4455.2-a1
| \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( -\phi - 2\) , \( -8 \phi - 5\bigr] \)
|
| 4455.2-a2
| \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( 44 \phi - 47\) , \( 91 \phi + 310\bigr] \)
|
| 4455.2-a3
| \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( 44 \phi - 272\) , \( 1045 \phi - 1319\bigr] \)
|
| 4455.2-a4
| \( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( -491 \phi + 487\) , \( -10099 \phi + 14948\bigr] \)
|
| 4455.2-a5
| \( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( 184 \phi - 413\) , \( -1684 \phi + 3203\bigr] \)
|
| 4455.2-a6
| \( \bigl[\phi\) , \( -\phi - 1\) , \( \phi + 1\) , \( -46 \phi - 47\) , \( -179 \phi - 140\bigr] \)
|
| 4455.2-a7
| \( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( 139 \phi - 2033\) , \( 28079 \phi - 15418\bigr] \)
|
| 4455.2-a8
| \( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( -86 \phi - 143\) , \( -388 \phi - 1117\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\
3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\
4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\
12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\
6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\
2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\
12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\
4 & 12 & 4 & 3 & 6 & 2 & 12 & 1
\end{array}\right)\)
