Elliptic curve isogeny class with LMFDB label 2240.b (Cremona label 2240v)

• Label: 2240.b
• Number of curves: $1$
• Conductor: $2240$
• CM: no
• Rank: $1$

Rank

The elliptic curve 2240.b1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2240.b do not have complex multiplication.

Modular form 2240.2.a.b

Elliptic curves in class 2240.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2240.b1	2240v1	\([0, 0, 0, 2, -2]\)	\(13824/35\)	\(-2240\)	\([]\)	\(192\)	\(-0.67336\)	\(\Gamma_0(N)\)-optimal