Base field \(\Q(\sqrt{3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).
Elliptic curves in class 4056.1-e over \(\Q(\sqrt{3}) \)
Isogeny class 4056.1-e contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
4056.1-e1 | \( \bigl[0\) , \( 1\) , \( 0\) , \( 5\) , \( 14\bigr] \) |
4056.1-e2 | \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 60 a - 105\) , \( -270 a + 468\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)