Elliptic curve isogeny class with LMFDB label 186576.cc (Cremona label 186576k)

• Label: 186576.cc
• Number of curves: $1$
• Conductor: $186576$
• CM: no
• Rank: $0$

Rank

The elliptic curve 186576.cc1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(13\)	\(1\)
\(23\)	\(1 - T\)

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
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 19 T^{2}\)	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 186576.cc do not have complex multiplication.

Modular form 186576.2.a.cc

Elliptic curves in class 186576.cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
186576.cc1	186576k1	\([0, 1, 0, -69, 1587]\)	\(-53248/1587\)	\(-1098559488\)	\([]\)	\(55680\)	\(0.41521\)	\(\Gamma_0(N)\)-optimal