Base field \(\Q(\sqrt{-3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).
Elliptic curves in class 105625.2-a over \(\Q(\sqrt{-3}) \)
Isogeny class 105625.2-a contains 2 curves linked by isogenies of degree 3.
Curve label | Weierstrass Coefficients |
---|---|
105625.2-a1 | \( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 3 a\) , \( 3\bigr] \) |
105625.2-a2 | \( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 53 a\) , \( -132\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)