Elliptic curve isogeny class 2304.1-o over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2304.1-o
• Conductor: 2304.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2304.1-o over \(\Q(\sqrt{5}) \)

Isogeny class 2304.1-o contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2304.1-o1	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( \phi - 1\) , \( -\phi + 2\bigr] \)
2304.1-o2	\( \bigl[0\) , \( -\phi\) , \( 0\) , \( -18 \phi - 139\) , \( -513 \phi + 214\bigr] \)
2304.1-o3	\( \bigl[0\) , \( -\phi\) , \( 0\) , \( -18 \phi - 19\) , \( 63 \phi + 46\bigr] \)
2304.1-o4	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -19 \phi - 81\) , \( 203 \phi + 150\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph