Base field \(\Q(\sqrt{13}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); 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 729.3-e over \(\Q(\sqrt{13}) \)
Isogeny class 729.3-e contains 2 curves linked by isogenies of degree 3.
| Curve label | Weierstrass Coefficients |
|---|---|
| 729.3-e1 | \( \bigl[0\) , \( 0\) , \( a\) , \( 30 a - 93\) , \( 174 a - 358\bigr] \) |
| 729.3-e2 | \( \bigl[0\) , \( 0\) , \( a\) , \( -3\) , \( -a - 1\bigr] \) |