Base field \(\Q(\sqrt{2}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).
Elliptic curves in class 578.1-a over \(\Q(\sqrt{2}) \)
Isogeny class 578.1-a contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 578.1-a1 | \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
| 578.1-a2 | \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -4 a - 8\) , \( -3 a - 2\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
