Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-1764.1-a
Conductor 1764.1
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 1764.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 1764.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
1764.1-a1 \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 0\) , \( 64 \phi + 64\) , \( -64 \phi - 48\bigr] \)
1764.1-a2 \( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 0\) , \( -16 \phi - 16\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph