Elliptic curve isogeny class 2880.1-g over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2880.1-g
• Conductor: 2880.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2880.1-g over \(\Q(\sqrt{5}) \)

Isogeny class 2880.1-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2880.1-g1	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 150 \phi - 145\) , \( -1545 \phi + 335\bigr] \)
2880.1-g2	\( \bigl[0\) , \( \phi\) , \( 0\) , \( -22 \phi - 19\) , \( -455 \phi + 830\bigr] \)
2880.1-g3	\( \bigl[0\) , \( \phi\) , \( 0\) , \( 38 \phi - 79\) , \( -203 \phi + 290\bigr] \)
2880.1-g4	\( \bigl[0\) , \( \phi\) , \( 0\) , \( -2 \phi - 14\) , \( -15 \phi - 15\bigr] \)

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