Elliptic curve isogeny class with Cremona label 389136cs (LMFDB label 389136.cs)

• Label: 389136cs
• Number of curves: $1$
• Conductor: $389136$
• CM: no
• Rank: $1$

Rank

The elliptic curve 389136cs1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1\)
\(67\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 389136cs do not have complex multiplication.

Modular form 389136.2.a.cs

Elliptic curves in class 389136cs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
389136.cs1	389136cs1	\([0, 1, 0, 3227, 72851]\)	\(512000/603\)	\(-4375557255168\)	\([]\)	\(518400\)	\(1.1119\)	\(\Gamma_0(N)\)-optimal