Base field \(\Q(\sqrt{17}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 196.1-c over \(\Q(\sqrt{17}) \)
Isogeny class 196.1-c contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 196.1-c1 | \( \bigl[1\) , \( -a\) , \( 0\) , \( 1\) , \( -2 a - 3\bigr] \) |
| 196.1-c2 | \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 7 a - 14\) , \( 11 a - 27\bigr] \) |