Elliptic curve isogeny class 4356.3-l over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-4356.3-l
• Conductor: 4356.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 4356.3-l over \(\Q(\sqrt{5}) \)

Isogeny class 4356.3-l contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
4356.3-l1	\( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi\) , \( 3 \phi - 10\) , \( -10 \phi + 11\bigr] \)
4356.3-l2	\( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi\) , \( 38 \phi - 95\) , \( 1253 \phi - 1708\bigr] \)
4356.3-l3	\( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi\) , \( 1158 \phi - 2815\) , \( 41669 \phi - 56716\bigr] \)
4356.3-l4	\( \bigl[\phi + 1\) , \( -\phi + 1\) , \( \phi\) , \( 73 \phi - 180\) , \( -620 \phi + 801\bigr] \)

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