Elliptic curve isogeny class with LMFDB label 6050.p (Cremona label 6050p)

• Label: 6050.p
• Number of curves: $1$
• Conductor: $6050$
• CM: no
• Rank: $1$

Rank

The elliptic curve 6050.p1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6050.p do not have complex multiplication.

Modular form 6050.2.a.p

Elliptic curves in class 6050.p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6050.p1	6050p1	\([1, 1, 0, -621700, 188514000]\)	\(-38401771585/22528\)	\(-15589736800000000\)	\([]\)	\(79200\)	\(2.0521\)	\(\Gamma_0(N)\)-optimal