Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 1458.2-a over \(\Q(\sqrt{-2}) \)
Isogeny class 1458.2-a contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 1458.2-a1 | \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -3\) , \( 2\bigr] \) |
| 1458.2-a2 | \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 90 a - 48\) , \( 405 a + 128\bigr] \) |