Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-3249.1-f
Conductor 3249.1
Rank \( 1 \)

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 3249.1-f over \(\Q(\sqrt{5}) \)

Isogeny class 3249.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
3249.1-f1 \( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \)
3249.1-f2 \( \bigl[1\) , \( 0\) , \( 1\) , \( -2\) , \( -1\bigr] \)
3249.1-f3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -7\) , \( 5\bigr] \)
3249.1-f4 \( \bigl[1\) , \( 0\) , \( 1\) , \( -102\) , \( 385\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph