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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2304.1-c
• Conductor: 2304.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

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

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

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

Curve label	Weierstrass Coefficients
2304.1-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( \phi\) , \( \phi\bigr] \)
2304.1-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 121 \phi - 260\) , \( 941 \phi - 1668\bigr] \)
2304.1-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( \phi - 20\) , \( 29 \phi - 12\bigr] \)
2304.1-c4	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( 64 \phi - 144\) , \( 160 \phi - 188\bigr] \)