Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-361.3-a
Conductor 361.3
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 361.3-a over \(\Q(\sqrt{5}) \)

Isogeny class 361.3-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
361.3-a1 \( \bigl[0\) , \( -\phi - 1\) , \( \phi\) , \( -4 \phi - 25\) , \( -38 \phi + 19\bigr] \)
361.3-a2 \( \bigl[0\) , \( -1\) , \( \phi\) , \( 687 \phi - 1503\) , \( 12916 \phi - 23753\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph