Elliptic curve isogeny class 225.1-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-225.1-a
• Conductor: 225.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 225.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 225.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
225.1-a1	\( \bigl[0\) , \( -\phi + 1\) , \( 1\) , \( -2 \phi - 1\) , \( 2 \phi + 1\bigr] \)
225.1-a2	\( \bigl[0\) , \( \phi\) , \( 1\) , \( -8 \phi + 17\) , \( 76 \phi - 131\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph