Elliptic curve isogeny class with LMFDB label 6084.f (Cremona label 6084k)

• Label: 6084.f
• Number of curves: $1$
• Conductor: $6084$
• CM: no
• Rank: $1$

Rank

The elliptic curve 6084.f1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6084.f do not have complex multiplication.

Modular form 6084.2.a.f

Isogeny graph

Elliptic curves in class 6084.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6084.f1	6084k1	\([0, 0, 0, -1521, -22815]\)	\(1168128\)	\(333135504\)	\([]\)	\(2520\)	\(0.56213\)	\(\Gamma_0(N)\)-optimal