Elliptic curve isogeny class 361.3-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-361.3-b
• Conductor: 361.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 361.3-b over \(\Q(\sqrt{5}) \)

Isogeny class 361.3-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
361.3-b1	\( \bigl[0\) , \( -\phi + 1\) , \( \phi\) , \( -1\) , \( 0\bigr] \)
361.3-b2	\( \bigl[0\) , \( -\phi + 1\) , \( \phi\) , \( -30 \phi - 41\) , \( 179 \phi + 55\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph