Elliptic curve isogeny class 3249.1-j over number field \(\Q(\sqrt{5}) \)

• Base field: \(\Q(\sqrt{5}) \)
• Label: 2.2.5.1-3249.1-j
• Conductor: 3249.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3249.1-j over \(\Q(\sqrt{5}) \)

Isogeny class 3249.1-j contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
3249.1-j1	\( \bigl[0\) , \( \phi - 1\) , \( 1\) , \( -13 \phi + 5\) , \( 9 \phi + 8\bigr] \)
3249.1-j2	\( \bigl[0\) , \( \phi\) , \( 1\) , \( 240 \phi - 9\) , \( -11763 \phi - 7999\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph