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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2880.1-a
• Conductor: 2880.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
2880.1-a1	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( 14 \phi - 17\) , \( 35 \phi - 45\bigr] \)
2880.1-a2	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -11 \phi + 3\) , \( -9 \phi - 2\bigr] \)
2880.1-a3	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -\phi - 2\) , \( 2 \phi\bigr] \)
2880.1-a4	\( \bigl[0\) , \( -\phi + 1\) , \( 0\) , \( -16 \phi - 32\) , \( 68 \phi + 72\bigr] \)

Rank

Rank: \( 1 \)

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