Elliptic curve isogeny class 89.1-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-89.1-a
• Conductor: 89.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 89.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 89.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
89.1-a1	\( \bigl[\phi\) , \( -\phi\) , \( 1\) , \( 15 \phi - 31\) , \( 12 \phi - 36\bigr] \)
89.1-a2	\( \bigl[\phi + 1\) , \( \phi - 1\) , \( 0\) , \( 4 \phi\) , \( 5 \phi + 7\bigr] \)
89.1-a3	\( \bigl[\phi\) , \( -\phi\) , \( 1\) , \( -1\) , \( 0\bigr] \)
89.1-a4	\( \bigl[\phi\) , \( -\phi\) , \( 1\) , \( 10 \phi - 26\) , \( 32 \phi - 60\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph