Elliptic curve isogeny class 1024.1-i over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-1024.1-i
• Conductor: 1024.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 1024.1-i over \(\Q(\sqrt{5}) \)

Isogeny class 1024.1-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1024.1-i1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 \phi - 1\) , \( 4 \phi + 1\bigr] \)
1024.1-i2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -\phi - 1\) , \( \phi + 1\bigr] \)
1024.1-i3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -\phi - 11\) , \( -13 \phi + 9\bigr] \)
1024.1-i4	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( -7 \phi + 7\) , \( -9 \phi + 16\bigr] \)