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

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

Isogeny class 4096.1-u contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
4096.1-u1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 2 \phi - 4\) , \( 2 \phi - 2\bigr] \)
4096.1-u2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 2 \phi - 4\) , \( -2 \phi + 2\bigr] \)
4096.1-u3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -8 \phi - 9\) , \( 24 \phi + 9\bigr] \)
4096.1-u4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -8 \phi - 9\) , \( -24 \phi - 9\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph