Elliptic curve isogeny class 2401.1-d over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2401.1-d
• Conductor: 2401.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2401.1-d over \(\Q(\sqrt{5}) \)

Isogeny class 2401.1-d contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
2401.1-d1	\( \bigl[0\) , \( \phi - 1\) , \( 1\) , \( -1454 \phi - 1453\) , \( 37868 \phi + 28764\bigr] \)
2401.1-d2	\( \bigl[0\) , \( -\phi\) , \( 1\) , \( -16 \phi + 33\) , \( 58 \phi - 106\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph