Base field \(\Q(\sqrt{13}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).
Elliptic curves in class 81.4-c over \(\Q(\sqrt{13}) \)
Isogeny class 81.4-c contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 81.4-c1 | \( \bigl[0\) , \( a - 1\) , \( a\) , \( 3 a - 9\) , \( -10 a + 19\bigr] \) |
| 81.4-c2 | \( \bigl[0\) , \( a - 1\) , \( a\) , \( 2 a - 5\) , \( -a + 1\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
