Base field \(\Q(\sqrt{2}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).
Elliptic curves in class 2450.1-g over \(\Q(\sqrt{2}) \)
Isogeny class 2450.1-g contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
2450.1-g1 | \( \bigl[1\) , \( a\) , \( 1\) , \( -a\) , \( -2\bigr] \) |
2450.1-g2 | \( \bigl[1\) , \( a\) , \( 1\) , \( -6 a - 20\) , \( -24 a - 42\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)