Elliptic curve isogeny class with LMFDB label 48960.du (Cremona label 48960z)

• Label: 48960.du
• Number of curves: $1$
• Conductor: $48960$
• CM: no
• Rank: $1$

Rank

The elliptic curve 48960.du1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 48960.du do not have complex multiplication.

Modular form 48960.2.a.du

Elliptic curves in class 48960.du

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48960.du1	48960z1	\([0, 0, 0, -16092, 973944]\)	\(-22864543488/7099285\)	\(-143088872094720\)	\([]\)	\(122880\)	\(1.4297\)	\(\Gamma_0(N)\)-optimal