Base field \(\Q(\sqrt{5}) \)
Generator \(\phi\), with minimal polynomial \( x^{2} - x - 1 \); class number \(1\).
Elliptic curves in class 76.1-a over \(\Q(\sqrt{5}) \)
Isogeny class 76.1-a contains 2 curves linked by isogenies of degree 5.
Curve label | Weierstrass Coefficients |
---|---|
76.1-a1 | \( \bigl[1\) , \( 0\) , \( \phi\) , \( -29 \phi + 3\) , \( -28 \phi - 68\bigr] \) |
76.1-a2 | \( \bigl[\phi\) , \( 0\) , \( \phi\) , \( \phi\) , \( 0\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)