Base field \(\Q(\sqrt{17}) \)
Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).
Elliptic curves in class 676.5-c over \(\Q(\sqrt{17}) \)
Isogeny class 676.5-c contains 2 curves linked by isogenies of degree 3.
Curve label | Weierstrass Coefficients |
---|---|
676.5-c1 | \( \bigl[1\) , \( a\) , \( 0\) , \( 20 a - 52\) , \( -80 a + 208\bigr] \) |
676.5-c2 | \( \bigl[1\) , \( a\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
Rank
Rank: \( 1 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)