Elliptic curve isogeny class with LMFDB label 4864.f (Cremona label 4864d)

• Label: 4864.f
• Number of curves: $1$
• Conductor: $4864$
• CM: no
• Rank: $1$

Rank

The elliptic curve 4864.f1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4864.f do not have complex multiplication.

Modular form 4864.2.a.f

Elliptic curves in class 4864.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4864.f1	4864d1	\([0, -1, 0, 3, 37]\)	\(64/19\)	\(-622592\)	\([]\)	\(512\)	\(-0.20904\)	\(\Gamma_0(N)\)-optimal