Base field \(\Q(\sqrt{5}) \)
Generator \(\phi\), with minimal polynomial \( x^{2} - x - 1 \); class number \(1\).
Elliptic curves in class 1600.1-k over \(\Q(\sqrt{5}) \)
Isogeny class 1600.1-k contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
1600.1-k1 | \( \bigl[0\) , \( \phi\) , \( 0\) , \( \phi\) , \( 1\bigr] \) |
1600.1-k2 | \( \bigl[0\) , \( \phi\) , \( 0\) , \( 6 \phi - 15\) , \( -15 \phi + 26\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)