Base field \(\Q(\sqrt{13}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).
Elliptic curves in class 81.5-c over \(\Q(\sqrt{13}) \)
Isogeny class 81.5-c contains 2 curves linked by isogenies of degree 3.
Curve label | Weierstrass Coefficients |
---|---|
81.5-c1 | \( \bigl[0\) , \( -a\) , \( a + 1\) , \( -2 a - 3\) , \( 0\bigr] \) |
81.5-c2 | \( \bigl[0\) , \( -a\) , \( a + 1\) , \( -3 a - 6\) , \( 9 a + 9\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)