Base field \(\Q(\sqrt{-559}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 140 \); class number \(16\).
Rank
Rank \(r\) satisfies \(0 \le r \le 1\)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 52.2-c over \(\Q(\sqrt{-559}) \)
Isogeny class 52.2-c contains 2 curves linked by isogenies of degree 7.
| Curve label | Weierstrass Coefficients |
|---|---|
| 52.2-c1 | \( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \) |
| 52.2-c2 | \( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \) |