Properties

Base field \(\Q(\sqrt{5}) \)
Label 2.2.5.1-1764.1-d
Conductor 1764.1
Rank \( 0 \)

Related objects

Learn more

Base field \(\Q(\sqrt{5}) \)

Generator \(\phi\), with minimal polynomial \( x^{2} - x - 1 \); class number \(1\).

Elliptic curves in class 1764.1-d over \(\Q(\sqrt{5}) \)

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

Curve label Weierstrass Coefficients
1764.1-d1 \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -14 \phi - 14\) , \( -314 \phi - 232\bigr] \)
1764.1-d2 \( \bigl[\phi\) , \( \phi - 1\) , \( \phi + 1\) , \( 33 \phi - 68\) , \( 113 \phi - 208\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph