Elliptic curve isogeny class 441.1-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-441.1-a
• Conductor: 441.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 441.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 441.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
441.1-a1	\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( -2 \phi + 3\) , \( 17 \phi - 30\bigr] \)
441.1-a2	\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -3 \phi - 3\) , \( -9 \phi - 6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph