Base field \(\Q(\sqrt{17}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).
Elliptic curves in class 576.7-q over \(\Q(\sqrt{17}) \)
Isogeny class 576.7-q contains 2 curves linked by isogenies of degree 5.
Curve label | Weierstrass Coefficients |
---|---|
576.7-q1 | \( \bigl[0\) , \( 1\) , \( a\) , \( 149 a - 397\) , \( -1421 a + 3657\bigr] \) |
576.7-q2 | \( \bigl[0\) , \( 1\) , \( a\) , \( -a + 3\) , \( -a + 1\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)