Base field \(\Q(\sqrt{17}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 118.4-b over \(\Q(\sqrt{17}) \)
Isogeny class 118.4-b contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 118.4-b1 | \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 3 a - 4\) , \( -6 a + 14\bigr] \) |
| 118.4-b2 | \( \bigl[1\) , \( a - 1\) , \( 0\) , \( -a - 1\) , \( 1\bigr] \) |