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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-4096.1-t
• Conductor: 4096.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
4096.1-t1	\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( \phi - 1\) , \( -\phi + 2\bigr] \)
4096.1-t2	\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( \phi - 6\) , \( 2 \phi - 1\bigr] \)
4096.1-t3	\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( 41 \phi - 86\) , \( 162 \phi - 297\bigr] \)
4096.1-t4	\( \bigl[0\) , \( \phi - 1\) , \( 0\) , \( -39 \phi - 6\) , \( 114 \phi + 23\bigr] \)

Rank

Rank: \( 1 \)

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