Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-116.2-a
Conductor 116.2
Rank \( 0 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{5}) \)

Generator \(\phi\), with minimal polynomial \( x^{2} - x - 1 \); class number \(1\).

Elliptic curves in class 116.2-a over \(\Q(\sqrt{5}) \)

Isogeny class 116.2-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
116.2-a1 \( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( -10 \phi - 6\) , \( -2 \phi - 32\bigr] \)
116.2-a2 \( \bigl[1\) , \( -1\) , \( \phi + 1\) , \( -1\) , \( -\phi\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph