Base field \(\Q(\sqrt{-7}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).
Elliptic curves in class 16.5-CMa over \(\Q(\sqrt{-7}) \)
Isogeny class 16.5-CMa contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
16.5-CMa1 | \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) |
16.5-CMa2 | \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 15 a - 5\) , \( 22 a + 14\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)