Base field \(\Q(\sqrt{2}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).
Elliptic curves in class 686.2-c over \(\Q(\sqrt{2}) \)
Isogeny class 686.2-c contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 686.2-c1 | \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 30 a - 50\) , \( -122 a + 124\bigr] \) |
| 686.2-c2 | \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
