Elliptic curve isogeny class with LMFDB label 6664.c (Cremona label 6664b)

• Label: 6664.c
• Number of curves: $1$
• Conductor: $6664$
• CM: no
• Rank: $1$

Rank

The elliptic curve 6664.c1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6664.c do not have complex multiplication.

Modular form 6664.2.a.c

Elliptic curves in class 6664.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6664.c1	6664b1	\([0, 0, 0, -5243, -146314]\)	\(-3241463778/4913\)	\(-24158439424\)	\([]\)	\(5472\)	\(0.89246\)	\(\Gamma_0(N)\)-optimal