Elliptic curve isogeny class 79.2-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-79.2-a
• Conductor: 79.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 79.2-a over \(\Q(\sqrt{5}) \)

Isogeny class 79.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
79.2-a1	\( \bigl[\phi\) , \( \phi + 1\) , \( 0\) , \( 6 \phi - 19\) , \( 4 \phi - 43\bigr] \)
79.2-a2	\( \bigl[\phi\) , \( \phi + 1\) , \( 0\) , \( \phi + 1\) , \( 0\bigr] \)
79.2-a3	\( \bigl[1\) , \( 1\) , \( 0\) , \( 4 \phi - 8\) , \( 5 \phi - 10\bigr] \)
79.2-a4	\( \bigl[1\) , \( 1\) , \( 0\) , \( 19 \phi - 63\) , \( -134 \phi + 131\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph