Elliptic curve isogeny class 3969.1-g over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-3969.1-g
• Conductor: 3969.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3969.1-g over \(\Q(\sqrt{5}) \)

Isogeny class 3969.1-g contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
3969.1-g1	\( \bigl[0\) , \( 0\) , \( 1\) , \( -267 \phi - 267\) , \( 3019 \phi + 2264\bigr] \)
3969.1-g2	\( \bigl[0\) , \( 0\) , \( 1\) , \( -3 \phi + 6\) , \( 5 \phi - 9\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph