Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-2025.1-f
Conductor 2025.1
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 2025.1-f over \(\Q(\sqrt{5}) \)

Isogeny class 2025.1-f contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
2025.1-f1 \( \bigl[0\) , \( 0\) , \( 1\) , \( -15 \phi - 15\) , \( -41 \phi - 31\bigr] \)
2025.1-f2 \( \bigl[0\) , \( 0\) , \( 1\) , \( -75 \phi + 150\) , \( -1975 \phi + 3456\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph