Elliptic curve isogeny class 76.2-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-76.2-a
• Conductor: 76.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 76.2-a over \(\Q(\sqrt{5}) \)

Isogeny class 76.2-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
76.2-a1	\( \bigl[\phi + 1\) , \( -\phi\) , \( \phi + 1\) , \( -3 \phi + 1\) , \( -\phi\bigr] \)
76.2-a2	\( \bigl[1\) , \( 0\) , \( \phi + 1\) , \( 28 \phi - 26\) , \( 27 \phi - 96\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph