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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-256.1-b
• 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-b over \(\Q(\sqrt{5}) \)

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

Curve label	Weierstrass Coefficients
256.1-b1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 3 \phi - 11\) , \( -115 \phi - 57\bigr] \)
256.1-b2	\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( 6 \phi - 5\) , \( 3 \phi - 7\bigr] \)
256.1-b3	\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( \phi\) , \( 0\bigr] \)
256.1-b4	\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( \phi - 5\) , \( -3 \phi + 4\bigr] \)
256.1-b5	\( \bigl[0\) , \( -\phi - 1\) , \( 0\) , \( -4 \phi\) , \( 8 \phi + 4\bigr] \)
256.1-b6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -3 \phi - 8\) , \( -115 \phi + 172\bigr] \)