Base field \(\Q(\sqrt{69}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 17 \); class number \(1\).
Elliptic curves in class 23.1-d over \(\Q(\sqrt{69}) \)
Isogeny class 23.1-d contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 23.1-d1 | \( \bigl[1\) , \( a\) , \( 1\) , \( a + 7\) , \( -2 a - 9\bigr] \) |
| 23.1-d2 | \( \bigl[1\) , \( a\) , \( 1\) , \( -14 a - 48\) , \( -82 a - 301\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
