Elliptic curve isogeny class with LMFDB label 56144.d (Cremona label 56144g)

• Label: 56144.d
• Number of curves: $1$
• Conductor: $56144$
• CM: no
• Rank: $1$

Rank

The elliptic curve 56144.d1 has rank \(1\).

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.b
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 56144.2.a.d

Elliptic curves in class 56144.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
56144.d1	56144g1	\([0, -1, 0, -9720, -365792]\)	\(-55990084/29\)	\(-52608275456\)	\([]\)	\(43200\)	\(1.0082\)	\(\Gamma_0(N)\)-optimal