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 27648.4-c over \(\Q(\sqrt{-2}) \)
Isogeny class 27648.4-c contains only one elliptic curve.
| Curve label | Weierstrass Coefficients |
|---|---|
| 27648.4-c1 | \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2 a - 5\) , \( 7 a + 3\bigr] \) |