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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-1280.1-i
• Conductor: 1280.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
1280.1-i1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -201 \phi - 374\) , \( 3072 \phi + 3418\bigr] \)
1280.1-i2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 \phi + 1\) , \( -36 \phi - 26\bigr] \)
1280.1-i3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 13\) , \( 34\bigr] \)
1280.1-i4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -7\) , \( 6\bigr] \)
1280.1-i5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)
1280.1-i6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( 426\bigr] \)
1280.1-i7	\( \bigl[0\) , \( 0\) , \( 0\) , \( -9 \phi + 10\) , \( 36 \phi - 62\bigr] \)
1280.1-i8	\( \bigl[0\) , \( 0\) , \( 0\) , \( 201 \phi - 575\) , \( -3072 \phi + 6490\bigr] \)

Rank

Rank: \( 1 \)

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