Elliptic curve isogeny class with LMFDB label 9280.j (Cremona label 9280s)

• Label: 9280.j
• Number of curves: $2$
• Conductor: $9280$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 9280.j have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9280.j do not have complex multiplication.

Modular form 9280.2.a.j

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 9280.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9280.j1	9280s2	\([0, 0, 0, -772, -8256]\)	\(12422690496/145\)	\(593920\)	\([2]\)	\(1536\)	\(0.25858\)
9280.j2	9280s1	\([0, 0, 0, -47, -136]\)	\(-179406144/21025\)	\(-1345600\)	\([2]\)	\(768\)	\(-0.087988\)	\(\Gamma_0(N)\)-optimal