Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-1764.1-b
Conductor 1764.1
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 1764.1-b over \(\Q(\sqrt{5}) \)

Isogeny class 1764.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
1764.1-b1 \( \bigl[\phi\) , \( 0\) , \( \phi + 1\) , \( -25 \phi - 58\) , \( 82 \phi - 58\bigr] \)
1764.1-b2 \( \bigl[1\) , \( 0\) , \( \phi + 1\) , \( 4 \phi - 16\) , \( 9 \phi - 26\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph