Elliptic curve isogeny class 164.2-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-164.2-a
• Conductor: 164.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 164.2-a over \(\Q(\sqrt{5}) \)

Isogeny class 164.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
164.2-a1	\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 0\) , \( \phi - 2\) , \( -\phi - 2\bigr] \)
164.2-a2	\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 0\) , \( \phi - 42\) , \( 7 \phi - 98\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph