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

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

Isogeny class 4096.1-y contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
4096.1-y1	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 57 \phi - 102\) , \( 110 \phi - 631\bigr] \)
4096.1-y2	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 17 \phi - 2\) , \( 2 \phi + 13\bigr] \)
4096.1-y3	\( \bigl[0\) , \( \phi\) , \( 0\) , \( 3 \phi - 5\) , \( -2 \phi + 3\bigr] \)
4096.1-y4	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -23 \phi - 22\) , \( -66 \phi - 55\bigr] \)
4096.1-y5	\( \bigl[0\) , \( \phi\) , \( 0\) , \( -17 \phi + 15\) , \( -2 \phi + 15\bigr] \)
4096.1-y6	\( \bigl[0\) , \( \phi\) , \( 0\) , \( -57 \phi - 45\) , \( -110 \phi - 521\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph