Base field \(\Q(\sqrt{3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).
Elliptic curves in class 47.1-a over \(\Q(\sqrt{3}) \)
Isogeny class 47.1-a contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
47.1-a1 | \( \bigl[a\) , \( -a - 1\) , \( a\) , \( a - 2\) , \( -1\bigr] \) |
47.1-a2 | \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 6 a - 12\) , \( 14 a - 25\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)