Base field \(\Q(\sqrt{-3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).
Elliptic curves in class 105625.2-e over \(\Q(\sqrt{-3}) \)
Isogeny class 105625.2-e contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
105625.2-e1 | \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -100 a\) , \( 125\bigr] \) |
105625.2-e2 | \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 25 a\) , \( 0\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)