Base field \(\Q(\sqrt{6}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).
Elliptic curves in class 768.1-b over \(\Q(\sqrt{6}) \)
Isogeny class 768.1-b contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
768.1-b1 | \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 34 a + 84\) , \( 240 a + 588\bigr] \) |
768.1-b2 | \( \bigl[0\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)