Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-49.1-a
Conductor 49.1
Rank \( 0 \)

Related objects

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

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

Elliptic curves in class 49.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 49.1-a contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
49.1-a1 \( \bigl[0\) , \( -\phi + 1\) , \( 1\) , \( -30 \phi - 29\) , \( -102 \phi - 84\bigr] \)
49.1-a2 \( \bigl[0\) , \( \phi\) , \( 1\) , \( 1\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph