Base field \(\Q(\sqrt{7}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).
Elliptic curves in class 222.4-a over \(\Q(\sqrt{7}) \)
Isogeny class 222.4-a contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 222.4-a1 | \( \bigl[1\) , \( 0\) , \( a\) , \( a - 5\) , \( 4 a - 12\bigr] \) |
| 222.4-a2 | \( \bigl[1\) , \( 0\) , \( a\) , \( 171 a - 450\) , \( 1991 a - 5267\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
