Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 6912.2-c over \(\Q(\sqrt{-2}) \)
Isogeny class 6912.2-c contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 6912.2-c1 | \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 18\) , \( 26 a - 14\bigr] \) |
| 6912.2-c2 | \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 7\) , \( 7 a\bigr] \) |