Elliptic curve isogeny class with Cremona label 7406f (LMFDB label 7406.g)

• Label: 7406f
• Number of curves: $1$
• Conductor: $7406$
• CM: no
• Rank: $1$

Rank

The elliptic curve 7406f1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(7\)	\(1 - T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7406f do not have complex multiplication.

Modular form 7406.2.a.f

Elliptic curves in class 7406f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7406.g1	7406f1	\([1, 1, 1, 35, 51]\)	\(8947391/6272\)	\(-3317888\)	\([]\)	\(2016\)	\(-0.060254\)	\(\Gamma_0(N)\)-optimal