Base field \(\Q(\sqrt{-3}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).
Elliptic curves in class 20164.1-c over \(\Q(\sqrt{-3}) \)
Isogeny class 20164.1-c contains 2 curves linked by isogenies of degree 2.
| Curve label | Weierstrass Coefficients |
|---|---|
| 20164.1-c1 | \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -a + 1\) , \( -3\bigr] \) |
| 20164.1-c2 | \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -41 a + 41\) , \( -91\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
