Base field \(\Q(\sqrt{-3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).
Elliptic curves in class 8112.2-a over \(\Q(\sqrt{-3}) \)
Isogeny class 8112.2-a contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 8112.2-a1 | \( \bigl[0\) , \( a\) , \( 0\) , \( -20 a + 20\) , \( -24\bigr] \) |
| 8112.2-a2 | \( \bigl[0\) , \( a\) , \( 0\) , \( -5 a + 5\) , \( 6\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
