Base field \(\Q(\sqrt{17}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).
Elliptic curves in class 676.4-c over \(\Q(\sqrt{17}) \)
Isogeny class 676.4-c contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 676.4-c1 | \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -20 a - 32\) , \( 80 a + 128\bigr] \) |
| 676.4-c2 | \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
