Base field \(\Q(\sqrt{19}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
Elliptic curves in class 54.3-c over \(\Q(\sqrt{19}) \)
Isogeny class 54.3-c contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 54.3-c1 | \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 3\) , \( -3 a - 14\bigr] \) |
| 54.3-c2 | \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 3 a + 21\) , \( 12 a - 14\bigr] \) |