Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Elliptic curves in class 5625.2-c over \(\Q(\sqrt{-2}) \)
Isogeny class 5625.2-c contains 2 curves linked by isogenies of degree 5.
Curve label | Weierstrass Coefficients |
---|---|
5625.2-c1 | \( \bigl[0\) , \( -1\) , \( 1\) , \( -8\) , \( -7\bigr] \) |
5625.2-c2 | \( \bigl[0\) , \( -1\) , \( 1\) , \( 42\) , \( 443\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)