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

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

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

Curve label	Weierstrass Coefficients
2401.1-c1	\( \bigl[\phi + 1\) , \( \phi\) , \( \phi\) , \( -2039213 \phi - 2039213\) , \( -2007731903 \phi - 1505289124\bigr] \)
2401.1-c2	\( \bigl[\phi\) , \( \phi - 1\) , \( \phi\) , \( 78 \phi - 157\) , \( -575 \phi + 986\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph