Elliptic curve isogeny class 1296.1-b over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-1296.1-b
• Conductor: 1296.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1296.1-b over \(\Q(\sqrt{5}) \)

Isogeny class 1296.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1296.1-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 21 \phi + 21\) , \( 328 \phi + 246\bigr] \)
1296.1-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -24 \phi - 159\) , \( -680 \phi + 246\bigr] \)
1296.1-b3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 \phi - 48\) , \( -76 \phi + 133\bigr] \)
1296.1-b4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 \phi - 183\) , \( 680 \phi - 434\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph