Base field \(\Q(\sqrt{5}) \)
Generator \(\phi\), with minimal polynomial \( x^{2} - x - 1 \); class number \(1\).
Elliptic curves in class 4096.1-e over \(\Q(\sqrt{5}) \)
Isogeny class 4096.1-e contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
4096.1-e1 | \( \bigl[0\) , \( 1\) , \( 0\) , \( 4 \phi - 5\) , \( -4 \phi + 3\bigr] \) |
4096.1-e2 | \( \bigl[0\) , \( 1\) , \( 0\) , \( -\phi\) , \( -\phi\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)