Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-179.2-b
Conductor 179.2
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 179.2-b over \(\Q(\sqrt{5}) \)

Isogeny class 179.2-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
179.2-b1 \( \bigl[1\) , \( 1\) , \( \phi + 1\) , \( 4 \phi - 14\) , \( 11 \phi - 29\bigr] \)
179.2-b2 \( \bigl[1\) , \( 1\) , \( \phi + 1\) , \( -\phi + 1\) , \( -\phi\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph