Elliptic curve isogeny class with Cremona label 56144b (LMFDB label 56144.p)

• Label: 56144b
• Number of curves: $1$
• Conductor: $56144$
• CM: no
• Rank: $0$

Rank

The elliptic curve 56144b1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 56144b do not have complex multiplication.

Modular form 56144.2.a.b

Elliptic curves in class 56144b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
56144.p1	56144b1	\([0, 1, 0, -7920337, 8576892619]\)	\(-91029177187328/841\)	\(-507656706081536\)	\([]\)	\(1140480\)	\(2.4026\)	\(\Gamma_0(N)\)-optimal