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

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

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

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

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

Isogeny class 1280.1-f contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
1280.1-f1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -36\) , \( 140\bigr] \)
1280.1-f2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4\) , \( -4\bigr] \)
1280.1-f3	\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( -98 \phi - 157\) , \( 563 \phi + 725\bigr] \)
1280.1-f4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
1280.1-f5	\( \bigl[0\) , \( -1\) , \( 0\) , \( 5 \phi - 16\) , \( 17 \phi - 16\bigr] \)
1280.1-f6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \)
1280.1-f7	\( \bigl[0\) , \( -1\) , \( 0\) , \( -5 \phi - 11\) , \( -17 \phi + 1\bigr] \)
1280.1-f8	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( 100 \phi - 256\) , \( -464 \phi + 1032\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 6 & 12 & 2 & 12 & 4 \\ 3 & 1 & 12 & 2 & 4 & 6 & 4 & 12 \\ 4 & 12 & 1 & 6 & 12 & 2 & 3 & 4 \\ 6 & 2 & 6 & 1 & 2 & 3 & 2 & 6 \\ 12 & 4 & 12 & 2 & 1 & 6 & 4 & 3 \\ 2 & 6 & 2 & 3 & 6 & 1 & 6 & 2 \\ 12 & 4 & 3 & 2 & 4 & 6 & 1 & 12 \\ 4 & 12 & 4 & 6 & 3 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph