Base field \(\Q(\sqrt{-3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).
Elliptic curves in class 36864.1-x over \(\Q(\sqrt{-3}) \)
Isogeny class 36864.1-x contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
36864.1-x1 | \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a + 8\) , \( 18 a - 13\bigr] \) |
36864.1-x2 | \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3\) , \( -a + 1\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)