Base field \(\Q(\sqrt{5}) \)
Generator \(\phi\), with minimal polynomial \( x^{2} - x - 1 \); class number \(1\).
Elliptic curves in class 225.1-c over \(\Q(\sqrt{5}) \)
Isogeny class 225.1-c contains 2 curves linked by isogenies of degree 5.
Curve label | Weierstrass Coefficients |
---|---|
225.1-c1 | \( \bigl[0\) , \( -1\) , \( 1\) , \( -8\) , \( -7\bigr] \) |
225.1-c2 | \( \bigl[0\) , \( 1\) , \( 1\) , \( 2\) , \( 4\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)