Base field \(\Q(\sqrt{6}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).
Elliptic curves in class 768.1-a over \(\Q(\sqrt{6}) \)
Isogeny class 768.1-a contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
768.1-a1 | \( \bigl[0\) , \( 1\) , \( 0\) , \( 2\) , \( 2\bigr] \) |
768.1-a2 | \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 66 a - 161\) , \( -305 a + 747\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)