Elliptic curve isogeny class 4961.4-f over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-4961.4-f
• Conductor: 4961.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 4961.4-f over \(\Q(\sqrt{5}) \)

Isogeny class 4961.4-f contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
4961.4-f1	\( \bigl[0\) , \( -\phi\) , \( \phi\) , \( -2 \phi - 3\) , \( 8 \phi - 2\bigr] \)
4961.4-f2	\( \bigl[0\) , \( -\phi\) , \( \phi\) , \( 218 \phi - 553\) , \( -3809 \phi + 4519\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph