Elliptic curve isogeny class with LMFDB label 40401.a (Cremona label 40401q)

• Label: 40401.a
• Number of curves: $1$
• Conductor: $40401$
• CM: no
• Rank: $1$

Rank

The elliptic curve 40401.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(67\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 40401.a do not have complex multiplication.

Modular form 40401.2.a.a

Elliptic curves in class 40401.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40401.a1	40401q1	\([0, 0, 1, 67335, 6842358]\)	\(512000/603\)	\(-39764328842524203\)	\([]\)	\(430848\)	\(1.8714\)	\(\Gamma_0(N)\)-optimal