Base field \(\Q(\sqrt{-7}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).
Elliptic curves in class 28672.6-e over \(\Q(\sqrt{-7}) \)
Isogeny class 28672.6-e contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
28672.6-e1 | \( \bigl[0\) , \( 1\) , \( 0\) , \( -a + 3\) , \( -a + 3\bigr] \) |
28672.6-e2 | \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 1\) , \( 3 a - 1\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)