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

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-2401.1-a
• 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-a over \(\Q(\sqrt{5}) \)

Isogeny class 2401.1-a contains 2 curves linked by isogenies of degree 37.

Curve label	Weierstrass Coefficients
2401.1-a1	\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -41617 \phi - 41617\) , \( 5859391 \phi + 4394543\bigr] \)
2401.1-a2	\( \bigl[\phi + 1\) , \( -\phi - 1\) , \( 1\) , \( -2 \phi - 2\) , \( -\phi - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)

Isogeny graph