Elliptic curve isogeny class 2420.1-d over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2420.1-d
• Conductor: 2420.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2420.1-d over \(\Q(\sqrt{5}) \)

Isogeny class 2420.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
2420.1-d1	\( \bigl[\phi\) , \( -\phi + 1\) , \( 1\) , \( -2 \phi + 1\) , \( 6 \phi + 4\bigr] \)
2420.1-d2	\( \bigl[\phi\) , \( -\phi + 1\) , \( 1\) , \( 13 \phi - 9\) , \( -150 \phi - 134\bigr] \)
2420.1-d3	\( \bigl[\phi\) , \( -\phi + 1\) , \( 1\) , \( -187 \phi - 409\) , \( -2230 \phi - 3494\bigr] \)
2420.1-d4	\( \bigl[1\) , \( \phi\) , \( \phi\) , \( 7 \phi - 25\) , \( 16 \phi - 15\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph