Base field \(\Q(\sqrt{33}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 8 \); class number \(1\).
Elliptic curves in class 128.5-a over \(\Q(\sqrt{33}) \)
Isogeny class 128.5-a contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
128.5-a1 | \( \bigl[a\) , \( 0\) , \( a\) , \( a - 4\) , \( 0\bigr] \) |
128.5-a2 | \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -88 a - 209\) , \( -87 a - 207\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)