Base field \(\Q(\sqrt{19}) \)
Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).
Elliptic curves in class 9.3-c over \(\Q(\sqrt{19}) \)
Isogeny class 9.3-c contains 2 curves linked by isogenies of degree 19.
| Curve label | Weierstrass Coefficients |
|---|---|
| 9.3-c1 | \( \bigl[0\) , \( 0\) , \( a\) , \( 16 a - 70\) , \( 73 a - 323\bigr] \) |
| 9.3-c2 | \( \bigl[0\) , \( 0\) , \( 1\) , \( 16 a - 70\) , \( -73 a + 318\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 19 \\ 19 & 1 \end{array}\right)\)
Isogeny graph
