Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-1369.1-a
Conductor 1369.1
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 1369.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 1369.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
1369.1-a1 \( \bigl[0\) , \( 1\) , \( 1\) , \( -23\) , \( -50\bigr] \)
1369.1-a2 \( \bigl[0\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \)
1369.1-a3 \( \bigl[0\) , \( 1\) , \( 1\) , \( -1873\) , \( -31833\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph