Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-4096.1-bd
Conductor 4096.1
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 4096.1-bd over \(\Q(\sqrt{5}) \)

Isogeny class 4096.1-bd contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
4096.1-bd1 \( \bigl[0\) , \( -1\) , \( 0\) , \( \phi - 1\) , \( -\phi + 1\bigr] \)
4096.1-bd2 \( \bigl[0\) , \( -1\) , \( 0\) , \( -4 \phi - 1\) , \( -4 \phi + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph