Properties

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

Isogeny class 4096.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
4096.1-d1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
4096.1-d2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \)
4096.1-d3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -44\) , \( -112\bigr] \)
4096.1-d4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -44\) , \( 112\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph