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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-4096.1-v
• 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-v over \(\Q(\sqrt{5}) \)

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

Curve label	Weierstrass Coefficients
4096.1-v1	\( \bigl[0\) , \( 0\) , \( 0\) , \( \phi + 1\) , \( 0\bigr] \)
4096.1-v2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 \phi - 4\) , \( 0\bigr] \)
4096.1-v3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -44 \phi - 44\) , \( -224 \phi - 112\bigr] \)
4096.1-v4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -44 \phi - 44\) , \( 224 \phi + 112\bigr] \)

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