Base field \(\Q(\sqrt{5}) \)
Generator \(\phi\), with minimal polynomial \( x^{2} - x - 1 \); class number \(1\).
Rank
Rank: \( 2 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 4205.1-c over \(\Q(\sqrt{5}) \)
Isogeny class 4205.1-c contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 4205.1-c1 | \( \bigl[1\) , \( -1\) , \( 1\) , \( 2\) , \( 6\bigr] \) |
| 4205.1-c2 | \( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 2\bigr] \) |