Base field \(\Q(\sqrt{2}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).
Elliptic curves in class 1568.3-g over \(\Q(\sqrt{2}) \)
Isogeny class 1568.3-g contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 1568.3-g1 | \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 5\) , \( 0\bigr] \) |
| 1568.3-g2 | \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 5\) , \( 0\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
