Elliptic curve isogeny class 361.2-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-361.2-a
• Conductor: 361.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 361.2-a over \(\Q(\sqrt{5}) \)

Isogeny class 361.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
361.2-a1	\( \bigl[0\) , \( \phi + 1\) , \( \phi + 1\) , \( 6 \phi - 30\) , \( 42 \phi - 49\bigr] \)
361.2-a2	\( \bigl[0\) , \( -1\) , \( \phi + 1\) , \( -687 \phi - 816\) , \( -12917 \phi - 10837\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph