Elliptic curve isogeny class with LMFDB label 6760.f (Cremona label 6760k)

• Label: 6760.f
• Number of curves: $1$
• Conductor: $6760$
• CM: no
• Rank: $1$

Rank

The elliptic curve 6760.f1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6760.f do not have complex multiplication.

Modular form 6760.2.a.f

Elliptic curves in class 6760.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6760.f1	6760k1	\([0, -1, 0, -9520, 359657]\)	\(7311616/25\)	\(326292288400\)	\([]\)	\(9984\)	\(1.0728\)	\(\Gamma_0(N)\)-optimal