Base field \(\Q(\sqrt{17}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).
Elliptic curves in class 512.1-h over \(\Q(\sqrt{17}) \)
Isogeny class 512.1-h contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 512.1-h1 | \( \bigl[0\) , \( -a\) , \( 0\) , \( a - 1\) , \( -4\bigr] \) |
| 512.1-h2 | \( \bigl[0\) , \( a\) , \( 0\) , \( 7 a - 16\) , \( 22 a - 56\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
