Base field \(\Q(\sqrt{2}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).
Elliptic curves in class 574.2-e over \(\Q(\sqrt{2}) \)
Isogeny class 574.2-e contains only one elliptic curve.
Curve label | Weierstrass Coefficients |
---|---|
574.2-e1 | \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 10 a - 14\) , \( 21 a - 30\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{r} 1 \end{array}\right)\)