Elliptic curves in class 3025.3-e over \(\Q(\sqrt{5}) \)
Isogeny class 3025.3-e contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 3025.3-e1
| \( \bigl[1\) , \( \phi - 1\) , \( 1\) , \( -651 \phi - 888\) , \( 41894 \phi + 21992\bigr] \)
|
| 3025.3-e2
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( 2738 \phi - 1937\) , \( -25841 \phi - 75109\bigr] \)
|
| 3025.3-e3
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -12 \phi - 12\) , \( 9 \phi - 34\bigr] \)
|
| 3025.3-e4
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -137 \phi - 1437\) , \( -19466 \phi + 6641\bigr] \)
|
| 3025.3-e5
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( 6588 \phi - 17337\) , \( -461031 \phi + 924911\bigr] \)
|
| 3025.3-e6
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -87 \phi - 262\) , \( 1694 \phi - 64\bigr] \)
|
| 3025.3-e7
| \( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( -238 \phi + 150\) , \( -9269 \phi + 13517\bigr] \)
|
| 3025.3-e8
| \( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 637 \phi - 1975\) , \( -159 \phi + 11012\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 6 & 12 & 2 & 12 & 4 \\
3 & 1 & 12 & 2 & 4 & 6 & 4 & 12 \\
4 & 12 & 1 & 6 & 12 & 2 & 3 & 4 \\
6 & 2 & 6 & 1 & 2 & 3 & 2 & 6 \\
12 & 4 & 12 & 2 & 1 & 6 & 4 & 3 \\
2 & 6 & 2 & 3 & 6 & 1 & 6 & 2 \\
12 & 4 & 3 & 2 & 4 & 6 & 1 & 12 \\
4 & 12 & 4 & 6 & 3 & 2 & 12 & 1
\end{array}\right)\)
