Elliptic curve isogeny class with LMFDB label 81144.x (Cremona label 81144n)

• Label: 81144.x
• Number of curves: $1$
• Conductor: $81144$
• CM: no
• Rank: $1$

Rank

The elliptic curve 81144.x1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 81144.x do not have complex multiplication.

Modular form 81144.2.a.x

Elliptic curves in class 81144.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
81144.x1	81144n1	\([0, 0, 0, 40740, -45560396]\)	\(116822144000/14076282141\)	\(-901051422850720512\)	\([]\)	\(788480\)	\(2.1246\)	\(\Gamma_0(N)\)-optimal