Elliptic curve isogeny class with LMFDB label 40344.a (Cremona label 40344c)

• Label: 40344.a
• Number of curves: $1$
• Conductor: $40344$
• CM: no
• Rank: $0$

Rank

The elliptic curve 40344.a1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 40344.a do not have complex multiplication.

Modular form 40344.2.a.a

Elliptic curves in class 40344.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40344.a1	40344c1	\([0, -1, 0, 11207, 1701421]\)	\(128000/1107\)	\(-1346141541065472\)	\([]\)	\(161280\)	\(1.5843\)	\(\Gamma_0(N)\)-optimal