Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Elliptic curves in class 27378.3-e over \(\Q(\sqrt{-2}) \)
Isogeny class 27378.3-e contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 27378.3-e1 | \( \bigl[1\) , \( -1\) , \( 1\) , \( -29\) , \( -107\bigr] \) |
| 27378.3-e2 | \( \bigl[1\) , \( -1\) , \( 1\) , \( -569\) , \( -5075\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
