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

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

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

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

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

Isogeny class 2304.1-l contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
2304.1-l1	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( \phi - 9\) , \( -17 \phi + 4\bigr] \)
2304.1-l2	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( \phi - 89\) , \( 1375 \phi - 732\bigr] \)
2304.1-l3	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( \phi - 2649\) , \( 45919 \phi - 24284\bigr] \)
2304.1-l4	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( \phi - 169\) , \( -817 \phi + 324\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph