Properties

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

Isogeny class 2025.1-d contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
2025.1-d1 \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 1\bigr] \)
2025.1-d2 \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -34\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph