Base field \(\Q(\sqrt{13}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).
Elliptic curves in class 17.1-a over \(\Q(\sqrt{13}) \)
Isogeny class 17.1-a contains 2 curves linked by isogenies of degree 3.
Curve label | Weierstrass Coefficients |
---|---|
17.1-a1 | \( \bigl[0\) , \( 1\) , \( a\) , \( -9 a + 18\) , \( 12 a - 32\bigr] \) |
17.1-a2 | \( \bigl[0\) , \( 1\) , \( a\) , \( a - 2\) , \( -a + 1\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)