Elliptic curve isogeny class with LMFDB label 48400.cs (Cremona label 48400c)

• Label: 48400.cs
• Number of curves: $1$
• Conductor: $48400$
• CM: no
• Rank: $1$

Rank

The elliptic curve 48400.cs1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 48400.cs do not have complex multiplication.

Modular form 48400.2.a.cs

Elliptic curves in class 48400.cs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48400.cs1	48400c1	\([0, 1, 0, 44367, -2967637]\)	\(1024\)	\(-9431790764000000\)	\([]\)	\(295680\)	\(1.7523\)	\(\Gamma_0(N)\)-optimal