Elliptic curves in class 2025.1-e over \(\Q(\sqrt{5}) \)
Isogeny class 2025.1-e contains
8 curves linked by isogenies of
degrees dividing 30.
| Curve label |
Weierstrass Coefficients |
| 2025.1-e1
| \( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( -6 \phi + 6\) , \( -7 \phi + 10\bigr] \)
|
| 2025.1-e2
| \( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -59 \phi + 51\) , \( 253 \phi - 264\bigr] \)
|
| 2025.1-e3
| \( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( 6 \phi - 1\) , \( 13 \phi + 2\bigr] \)
|
| 2025.1-e4
| \( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( 59 \phi - 8\) , \( -194 \phi - 19\bigr] \)
|
| 2025.1-e5
| \( \bigl[\phi + 1\) , \( 1\) , \( \phi + 1\) , \( 6 \phi - 76\) , \( 178 \phi - 193\bigr] \)
|
| 2025.1-e6
| \( \bigl[\phi + 1\) , \( 1\) , \( \phi\) , \( 59 \phi - 683\) , \( -5324 \phi + 3896\bigr] \)
|
| 2025.1-e7
| \( \bigl[\phi\) , \( -\phi - 1\) , \( 0\) , \( -6 \phi - 69\) , \( -172 \phi + 55\bigr] \)
|
| 2025.1-e8
| \( \bigl[\phi\) , \( -\phi - 1\) , \( 1\) , \( -59 \phi - 624\) , \( 5383 \phi - 804\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 15 & 5 & 3 & 10 & 6 & 2 & 30 \\
15 & 1 & 3 & 5 & 6 & 10 & 30 & 2 \\
5 & 3 & 1 & 15 & 2 & 30 & 10 & 6 \\
3 & 5 & 15 & 1 & 30 & 2 & 6 & 10 \\
10 & 6 & 2 & 30 & 1 & 15 & 5 & 3 \\
6 & 10 & 30 & 2 & 15 & 1 & 3 & 5 \\
2 & 30 & 10 & 6 & 5 & 3 & 1 & 15 \\
30 & 2 & 6 & 10 & 3 & 5 & 15 & 1
\end{array}\right)\)
