Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Elliptic curves in class 27225.4-b over \(\Q(\sqrt{-2}) \)
Isogeny class 27225.4-b contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 27225.4-b1 | \( \bigl[a\) , \( 0\) , \( 1\) , \( -4 a - 4\) , \( 3 a - 13\bigr] \) |
| 27225.4-b2 | \( \bigl[a\) , \( 0\) , \( 1\) , \( 8 a + 10\) , \( -5 a + 18\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
