Base field \(\Q(\sqrt{-19}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 5 \); class number \(1\).
Elliptic curves in class 85.2-a over \(\Q(\sqrt{-19}) \)
Isogeny class 85.2-a contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 85.2-a1 | \( \bigl[1\) , \( -a\) , \( 0\) , \( 4\) , \( -4 a + 1\bigr] \) |
| 85.2-a2 | \( \bigl[1\) , \( -a\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
