Base field \(\Q(\sqrt{5}) \)
Generator \(\phi\), with minimal polynomial \( x^{2} - x - 1 \); class number \(1\).
Elliptic curves in class 405.1-a over \(\Q(\sqrt{5}) \)
Isogeny class 405.1-a contains 10 curves linked by isogenies of degrees dividing 32.
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rrrrrrrrrr} 1 & 8 & 32 & 16 & 8 & 16 & 4 & 32 & 2 & 4 \\ 8 & 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 & 8 \\ 32 & 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 & 32 \\ 16 & 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 & 16 \\ 8 & 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 & 8 \\ 16 & 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 & 16 \\ 4 & 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 & 4 \\ 32 & 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 & 32 \\ 2 & 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 & 2 \\ 4 & 8 & 32 & 16 & 8 & 16 & 4 & 32 & 2 & 1 \end{array}\right)\)