Base field \(\Q(\sqrt{-3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).
Elliptic curves in class 49152.1-f over \(\Q(\sqrt{-3}) \)
Isogeny class 49152.1-f contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
49152.1-f1 | \( \bigl[0\) , \( a\) , \( 0\) , \( 5 a - 4\) , \( 3 a - 3\bigr] \) |
49152.1-f2 | \( \bigl[0\) , \( a\) , \( 0\) , \( 35 a - 19\) , \( -48 a - 27\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)