Base field \(\Q(\sqrt{2}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{r} 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 313.1-c over \(\Q(\sqrt{2}) \)
Isogeny class 313.1-c contains only one elliptic curve.
| Curve label | Weierstrass Coefficients |
|---|---|
| 313.1-c1 | \( \bigl[1\) , \( -a\) , \( a\) , \( -a\) , \( a + 1\bigr] \) |