Base field \(\Q(\sqrt{3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).
Elliptic curves in class 47.1-b over \(\Q(\sqrt{3}) \)
Isogeny class 47.1-b contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
47.1-b1 | \( \bigl[1\) , \( a\) , \( 1\) , \( a - 1\) , \( 0\bigr] \) |
47.1-b2 | \( \bigl[1\) , \( a\) , \( 1\) , \( 6 a - 11\) , \( -14 a + 24\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)