Elliptic curve isogeny class with LMFDB label 2040.e (Cremona label 2040d)

• Label: 2040.e
• Number of curves: $1$
• Conductor: $2040$
• CM: no
• Rank: $1$

Rank

The elliptic curve 2040.e1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2040.e do not have complex multiplication.

Modular form 2040.2.a.e

Elliptic curves in class 2040.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2040.e1	2040d1	\([0, -1, 0, 0, -3]\)	\(-256/255\)	\(-4080\)	\([]\)	\(96\)	\(-0.62816\)	\(\Gamma_0(N)\)-optimal