Base field \(\Q(\sqrt{-5}) \)
Generator \(a\), with minimal polynomial \( x^{2} + 5 \); class number \(2\).
Elliptic curves in class 16.1-b over \(\Q(\sqrt{-5}) \)
Isogeny class 16.1-b contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
16.1-b1 | \( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( a\bigr] \) |
16.1-b2 | \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -a + 3\) , \( -a + 1\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)