Base field \(\Q(\sqrt{17}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).
Elliptic curves in class 784.2-f over \(\Q(\sqrt{17}) \)
Isogeny class 784.2-f contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 784.2-f1 | \( \bigl[a\) , \( 1\) , \( 0\) , \( -4 a + 12\) , \( 0\bigr] \) |
| 784.2-f2 | \( \bigl[a\) , \( 1\) , \( 0\) , \( 16 a - 48\) , \( 24 a - 80\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
