Elliptic curve isogeny class with LMFDB label 6171.a (Cremona label 6171e)

• Label: 6171.a
• Number of curves: $1$
• Conductor: $6171$
• CM: no
• Rank: $1$

Rank

The elliptic curve 6171.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(11\)	\(1\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6171.a do not have complex multiplication.

Modular form 6171.2.a.a

Elliptic curves in class 6171.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6171.a1	6171e1	\([0, 1, 1, -4572, -158416]\)	\(-87367919423488/37321507107\)	\(-4515902359947\)	\([]\)	\(15504\)	\(1.1359\)	\(\Gamma_0(N)\)-optimal