Base field \(\Q(\sqrt{21}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).
Elliptic curves in class 17.2-b over \(\Q(\sqrt{21}) \)
Isogeny class 17.2-b contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 17.2-b1 | \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
| 17.2-b2 | \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 10 a - 25\) , \( -26 a + 76\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
