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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-4096.1-o
• Conductor: 4096.1
• Rank: \( 0 \)

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

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

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

Isogeny class 4096.1-o contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4096.1-o1	\( \bigl[0\) , \( 1\) , \( 0\) , \( \phi\) , \( \phi\bigr] \)
4096.1-o2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 \phi - 5\) , \( 4 \phi + 3\bigr] \)
4096.1-o3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 \phi - 45\) , \( -108 \phi + 27\bigr] \)
4096.1-o4	\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( -31 \phi + 26\) , \( -36 \phi + 133\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph