Base field \(\Q(\sqrt{13}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).
Elliptic curves in class 576.2-i over \(\Q(\sqrt{13}) \)
Isogeny class 576.2-i contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
576.2-i1 | \( \bigl[0\) , \( 0\) , \( 0\) , \( a - 6\) , \( a - 6\bigr] \) |
576.2-i2 | \( \bigl[0\) , \( 0\) , \( 0\) , \( -19 a - 21\) , \( -48 a - 90\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)