Base field \(\Q(\sqrt{-3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).
Elliptic curves in class 13456.1-b over \(\Q(\sqrt{-3}) \)
Isogeny class 13456.1-b contains 2 curves linked by isogenies of degree 3.
Curve label | Weierstrass Coefficients |
---|---|
13456.1-b1 | \( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
13456.1-b2 | \( \bigl[0\) , \( 1\) , \( 0\) , \( 36\) , \( -76\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)