Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Rank
Rank: \( 2 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 20000.1-a over \(\Q(\sqrt{-2}) \)
Isogeny class 20000.1-a contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 20000.1-a1 | \( \bigl[0\) , \( 1\) , \( 0\) , \( -8\) , \( 238\bigr] \) |
| 20000.1-a2 | \( \bigl[0\) , \( 1\) , \( 0\) , \( -158\) , \( -812\bigr] \) |