Base field \(\Q(\sqrt{-2}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).
Elliptic curves in class 36864.2-h over \(\Q(\sqrt{-2}) \)
Isogeny class 36864.2-h contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
36864.2-h1 | \( \bigl[0\) , \( a\) , \( 0\) , \( -2 a\) , \( 4 a - 4\bigr] \) |
36864.2-h2 | \( \bigl[0\) , \( a\) , \( 0\) , \( 2 a + 12\) , \( -8 a + 4\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)