Base field \(\Q(\sqrt{19}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{r} 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 54.4-e over \(\Q(\sqrt{19}) \)
Isogeny class 54.4-e contains only one elliptic curve.
| Curve label | Weierstrass Coefficients |
|---|---|
| 54.4-e1 | \( \bigl[a\) , \( -1\) , \( 1\) , \( 411 a - 1789\) , \( 10406 a - 45357\bigr] \) |