Base field \(\Q(\sqrt{209}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 52 \); class number \(1\).
Elliptic curves in class 19.1-b over \(\Q(\sqrt{209}) \)
Isogeny class 19.1-b contains 3 curves linked by isogenies of degrees dividing 9.
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)