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

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

Isogeny class 2401.1-e contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
2401.1-e1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)
2401.1-e2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -107\) , \( 552\bigr] \)
2401.1-e3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \)
2401.1-e4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1822\) , \( 30393\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph