Base field \(\Q(\sqrt{-2491}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x + 623 \); class number \(12\).
Rank
Rank \(r\) satisfies \(0 \le r \le 1\)Isogeny matrix
\(\left(\begin{array}{r} 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 4.1-c over \(\Q(\sqrt{-2491}) \)
Isogeny class 4.1-c contains only one elliptic curve.
| Curve label | Weierstrass Coefficients |
|---|---|
| 4.1-c1 | \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 20 a + 8145\) , \( -291 a - 142791\bigr] \) |