Base field \(\Q(\sqrt{5}) \)
Generator \(\phi\), with minimal polynomial \( x^{2} - x - 1 \); class number \(1\).
Elliptic curves in class 2025.1-c over \(\Q(\sqrt{5}) \)
Isogeny class 2025.1-c contains 2 curves linked by isogenies of degree 3.
Curve label | Weierstrass Coefficients |
---|---|
2025.1-c1 | \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -25 \phi - 19\bigr] \) |
2025.1-c2 | \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 675 \phi + 506\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)