Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Elliptic curves in class 225.1-a over \(\Q(\sqrt{-2}) \)
Isogeny class 225.1-a contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
225.1-a1 | \( \bigl[a\) , \( -1\) , \( 1\) , \( -3 a + 8\) , \( -4 a - 9\bigr] \) |
225.1-a2 | \( \bigl[a\) , \( -1\) , \( a + 1\) , \( 2 a + 2\) , \( 5\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)