Elliptic curve isogeny class 36.1-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-36.1-a
• Conductor: 36.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 36.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 36.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
36.1-a1	\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( 0\) , \( 0\bigr] \)
36.1-a2	\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -5 \phi - 5\) , \( -51 \phi - 37\bigr] \)
36.1-a3	\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 165 \phi - 331\) , \( 1352 \phi - 2408\bigr] \)
36.1-a4	\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 10 \phi - 21\) , \( -31 \phi + 51\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph