Base field \(\Q(\sqrt{13}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).
Elliptic curves in class 81.5-a over \(\Q(\sqrt{13}) \)
Isogeny class 81.5-a contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 81.5-a1 | \( \bigl[a\) , \( a\) , \( a + 1\) , \( 0\) , \( -2\bigr] \) |
| 81.5-a2 | \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 5 a + 6\) , \( 15 a + 19\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
