Base field \(\Q(\sqrt{17}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).
Elliptic curves in class 648.4-c over \(\Q(\sqrt{17}) \)
Isogeny class 648.4-c contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 648.4-c1 | \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 0\) , \( -5 a - 8\bigr] \) |
| 648.4-c2 | \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -9 a + 24\) , \( 14 a - 36\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
