Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-41.2-a
Conductor 41.2
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 41.2-a over \(\Q(\sqrt{5}) \)

Isogeny class 41.2-a contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
41.2-a1 \( \bigl[0\) , \( \phi - 1\) , \( \phi + 1\) , \( -10 \phi - 30\) , \( -32 \phi - 82\bigr] \)
41.2-a2 \( \bigl[0\) , \( \phi - 1\) , \( \phi + 1\) , \( 0\) , \( -\phi\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph