Base field \(\Q(\sqrt{-3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).
Elliptic curves in class 50052.2-a over \(\Q(\sqrt{-3}) \)
Isogeny class 50052.2-a contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
50052.2-a1 | \( \bigl[1\) , \( 1\) , \( 1\) , \( 2 a - 1\) , \( 2 a - 1\bigr] \) |
50052.2-a2 | \( \bigl[1\) , \( 1\) , \( 1\) , \( -8 a - 1\) , \( 6 a - 1\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)