Elliptic curves in class 275.1-a over \(\Q(\sqrt{5}) \)
Isogeny class 275.1-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 275.1-a1
| \( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi + 1\) , \( -\phi - 2\) , \( -\phi - 2\bigr] \)
|
| 275.1-a2
| \( \bigl[1\) , \( \phi + 1\) , \( \phi + 1\) , \( 24 \phi - 1\) , \( 379 \phi + 255\bigr] \)
|
| 275.1-a3
| \( \bigl[1\) , \( \phi + 1\) , \( \phi + 1\) , \( -101 \phi - 126\) , \( 159 \phi - 110\bigr] \)
|
| 275.1-a4
| \( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi + 1\) , \( -276 \phi - 2\) , \( -2201 \phi + 823\bigr] \)
|
| 275.1-a5
| \( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi + 1\) , \( -26 \phi - 127\) , \( 174 \phi + 448\bigr] \)
|
| 275.1-a6
| \( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi + 1\) , \( -\phi - 27\) , \( 4 \phi - 67\bigr] \)
|
| 275.1-a7
| \( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi + 1\) , \( -976 \phi - 1052\) , \( 24329 \phi + 11533\bigr] \)
|
| 275.1-a8
| \( \bigl[\phi\) , \( \phi\) , \( \phi\) , \( 32 \phi - 111\) , \( 596 \phi - 1187\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\
3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\
4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\
12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\
6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\
2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\
12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\
4 & 12 & 4 & 3 & 6 & 2 & 12 & 1
\end{array}\right)\)
