Base field \(\Q(\sqrt{17}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).
Elliptic curves in class 676.4-d over \(\Q(\sqrt{17}) \)
Isogeny class 676.4-d contains 2 curves linked by isogenies of degree 2.
Curve label | Weierstrass Coefficients |
---|---|
676.4-d1 | \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -9 a - 14\) , \( 8 a + 12\bigr] \) |
676.4-d2 | \( \bigl[1\) , \( a - 1\) , \( a\) , \( -3\) , \( -7 a + 13\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)