Elliptic curve isogeny class 256.1-a over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-256.1-a
• Conductor: 256.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 256.1-a over \(\Q(\sqrt{5}) \)

Isogeny class 256.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
256.1-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 3 \phi - 11\) , \( 115 \phi + 57\bigr] \)
256.1-a2	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( 6 \phi - 5\) , \( -3 \phi + 7\bigr] \)
256.1-a3	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( \phi\) , \( 0\bigr] \)
256.1-a4	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( \phi - 5\) , \( 3 \phi - 4\bigr] \)
256.1-a5	\( \bigl[0\) , \( \phi + 1\) , \( 0\) , \( -4 \phi\) , \( -8 \phi - 4\bigr] \)
256.1-a6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -3 \phi - 8\) , \( 115 \phi - 172\bigr] \)