Elliptic curve isogeny class with Cremona label 53371b (LMFDB label 53371.a)

• Label: 53371b
• Number of curves: $1$
• Conductor: $53371$
• CM: no
• Rank: $0$

Rank

The elliptic curve 53371b1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(19\)	\(1 + T\)
\(53\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 53371b do not have complex multiplication.

Modular form 53371.2.a.b

Elliptic curves in class 53371b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53371.a1	53371b1	\([0, 0, 1, 171349, -15594866]\)	\(25102282752/19266931\)	\(-427039216531525099\)	\([]\)	\(775008\)	\(2.0711\)	\(\Gamma_0(N)\)-optimal