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

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

Rank

The elliptic curve 40344c1 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 40344.2.a.c

Elliptic curves in class 40344c

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