Base field \(\Q(\sqrt{17}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).
Elliptic curves in class 676.5-d over \(\Q(\sqrt{17}) \)
Isogeny class 676.5-d contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
676.5-d1 | \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -a - 3\) , \( 6 a + 6\bigr] \) |
676.5-d2 | \( \bigl[1\) , \( a + 1\) , \( a\) , \( 10 a - 23\) , \( a - 3\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)