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

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

Rank

The elliptic curve 56144p1 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 \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 56144.2.a.p

Elliptic curves in class 56144p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
56144.h1	56144p1	\([0, 0, 0, -21296, -1171280]\)	\(1216512/29\)	\(25462405320704\)	\([]\)	\(105600\)	\(1.3573\)	\(\Gamma_0(N)\)-optimal