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 54.3-a over \(\Q(\sqrt{19}) \)
Isogeny class 54.3-a contains only one elliptic curve.
| Curve label | Weierstrass Coefficients |
|---|---|
| 54.3-a1 | \( \bigl[1\) , \( -1\) , \( 0\) , \( -4 a - 17\) , \( -8 a - 35\bigr] \) |