Elliptic curves in class 275.2-a over \(\Q(\sqrt{5}) \)
Isogeny class 275.2-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 275.2-a1
| \( \bigl[\phi + 1\) , \( \phi + 1\) , \( \phi\) , \( -30 \phi - 78\) , \( -706 \phi - 622\bigr] \)
|
| 275.2-a2
| \( \bigl[\phi\) , \( 1\) , \( \phi\) , \( 274 \phi - 276\) , \( 2200 \phi - 1377\bigr] \)
|
| 275.2-a3
| \( \bigl[\phi\) , \( 1\) , \( \phi\) , \( -\phi - 1\) , \( -2\bigr] \)
|
| 275.2-a4
| \( \bigl[\phi\) , \( 1\) , \( \phi\) , \( 24 \phi - 151\) , \( -175 \phi + 623\bigr] \)
|
| 275.2-a5
| \( \bigl[\phi\) , \( 1\) , \( \phi\) , \( 974 \phi - 2026\) , \( -24330 \phi + 35863\bigr] \)
|
| 275.2-a6
| \( \bigl[\phi\) , \( 1\) , \( \phi\) , \( -\phi - 26\) , \( -5 \phi - 62\bigr] \)
|
| 275.2-a7
| \( \bigl[1\) , \( -\phi - 1\) , \( \phi + 1\) , \( -23 \phi + 22\) , \( -357 \phi + 612\bigr] \)
|
| 275.2-a8
| \( \bigl[1\) , \( -\phi - 1\) , \( \phi + 1\) , \( 102 \phi - 228\) , \( -262 \phi + 277\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 6 & 12 & 2 & 12 & 4 \\
3 & 1 & 12 & 2 & 4 & 6 & 4 & 12 \\
4 & 12 & 1 & 6 & 12 & 2 & 3 & 4 \\
6 & 2 & 6 & 1 & 2 & 3 & 2 & 6 \\
12 & 4 & 12 & 2 & 1 & 6 & 4 & 3 \\
2 & 6 & 2 & 3 & 6 & 1 & 6 & 2 \\
12 & 4 & 3 & 2 & 4 & 6 & 1 & 12 \\
4 & 12 & 4 & 6 & 3 & 2 & 12 & 1
\end{array}\right)\)
