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

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

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

Curve label	Weierstrass Coefficients
4096.1-bb1	\( \bigl[0\) , \( \phi\) , \( 0\) , \( 39 \phi - 45\) , \( 114 \phi - 137\bigr] \)
4096.1-bb2	\( \bigl[0\) , \( \phi\) , \( 0\) , \( -\phi - 5\) , \( 2 \phi - 1\bigr] \)
4096.1-bb3	\( \bigl[0\) , \( \phi\) , \( 0\) , \( -\phi\) , \( -\phi - 1\bigr] \)
4096.1-bb4	\( \bigl[0\) , \( \phi\) , \( 0\) , \( -41 \phi - 45\) , \( 162 \phi + 135\bigr] \)

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