Elliptic curve isogeny class 1280.1-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-1280.1-a
• Conductor: 1280.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 1280.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 1280.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
1280.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 173 \phi - 547\) , \( 3764 \phi - 4110\bigr] \)
1280.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 \phi - 7\) , \( -16 \phi + 6\bigr] \)
1280.1-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 13 \phi + 13\) , \( 68 \phi + 34\bigr] \)
1280.1-a4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -7 \phi - 7\) , \( 12 \phi + 6\bigr] \)
1280.1-a5	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 \phi - 4\) , \( -2 \phi + 3\bigr] \)
1280.1-a6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -107 \phi - 107\) , \( 852 \phi + 426\bigr] \)
1280.1-a7	\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 \phi + 1\) , \( -16 \phi + 10\bigr] \)
1280.1-a8	\( \bigl[0\) , \( 0\) , \( 0\) , \( -173 \phi - 374\) , \( 3764 \phi + 346\bigr] \)