Base field \(\Q(\sqrt{-3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).
Elliptic curves in class 41772.1-e over \(\Q(\sqrt{-3}) \)
Isogeny class 41772.1-e contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 41772.1-e1 | \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -8 a\) , \( -7\bigr] \) |
| 41772.1-e2 | \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 2 a\) , \( -3\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
