Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Elliptic curves in class 54.4-a over \(\Q(\sqrt{-2}) \)
Isogeny class 54.4-a contains 4 curves linked by isogenies of degrees dividing 27.
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rrrr} 1 & 3 & 9 & 3 \\ 3 & 1 & 27 & 9 \\ 9 & 27 & 1 & 3 \\ 3 & 9 & 3 & 1 \end{array}\right)\)