Elliptic curve isogeny class 4356.2-l over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-4356.2-l
• Conductor: 4356.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 4356.2-l over \(\Q(\sqrt{5}) \)

Isogeny class 4356.2-l contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
4356.2-l1	\( \bigl[\phi\) , \( 1\) , \( \phi + 1\) , \( -5 \phi - 6\) , \( 9 \phi + 1\bigr] \)
4356.2-l2	\( \bigl[\phi\) , \( 1\) , \( \phi + 1\) , \( -40 \phi - 56\) , \( -1254 \phi - 455\bigr] \)
4356.2-l3	\( \bigl[\phi\) , \( 1\) , \( \phi + 1\) , \( -1160 \phi - 1656\) , \( -41670 \phi - 15047\bigr] \)
4356.2-l4	\( \bigl[\phi\) , \( 1\) , \( \phi + 1\) , \( -75 \phi - 106\) , \( 619 \phi + 181\bigr] \)

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