Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-4205.1-c
Conductor 4205.1
Rank \( 2 \)

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 4205.1-c over \(\Q(\sqrt{5}) \)

Isogeny class 4205.1-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
4205.1-c1 \( \bigl[1\) , \( -1\) , \( 1\) , \( 2\) , \( 6\bigr] \)
4205.1-c2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 2\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph