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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-441.1-b
• 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-b over \(\Q(\sqrt{5}) \)

Isogeny class 441.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
441.1-b1	\( \bigl[\phi\) , \( -\phi\) , \( \phi\) , \( -3\) , \( -2 \phi\bigr] \)
441.1-b2	\( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi + 1\) , \( -142 \phi - 199\) , \( -670 \phi + 101\bigr] \)
441.1-b3	\( \bigl[\phi\) , \( -\phi\) , \( \phi\) , \( -48\) , \( -101 \phi + 54\bigr] \)
441.1-b4	\( \bigl[1\) , \( -\phi + 1\) , \( \phi\) , \( 98 \phi - 269\) , \( -1112 \phi + 1370\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph