Base field \(\Q(\sqrt{21}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); 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 768.1-r over \(\Q(\sqrt{21}) \)
Isogeny class 768.1-r contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 768.1-r1 | \( \bigl[0\) , \( -1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
| 768.1-r2 | \( \bigl[0\) , \( -1\) , \( 0\) , \( -4 a - 8\) , \( 4 a + 8\bigr] \) |