Elliptic curve isogeny class 4096.1-q over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-4096.1-q
• Conductor: 4096.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 4096.1-q over \(\Q(\sqrt{5}) \)

Isogeny class 4096.1-q contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
4096.1-q1	\( \bigl[0\) , \( -\phi\) , \( 0\) , \( 3 \phi - 1\) , \( 6 \phi + 5\bigr] \)
4096.1-q2	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -\phi + 1\) , \( -\phi + 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph