Elliptic curve isogeny class 545.2-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-545.2-b
• Number of curves: 2
• Conductor: 545.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 545.2-b over \(\Q(\sqrt{5}) \)

Isogeny class 545.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
545.2-b1	\( \bigl[\phi + 1\) , \( \phi + 1\) , \( \phi\) , \( 11 \phi + 1\) , \( 73 \phi + 36\bigr] \)
545.2-b2	\( \bigl[\phi + 1\) , \( \phi + 1\) , \( \phi\) , \( -4 \phi - 9\) , \( 6 \phi - 4\bigr] \)