Elliptic curve isogeny class with LMFDB label 864.e (Cremona label 864a)

• Label: 864.e
• Number of curves: $1$
• Conductor: $864$
• CM: no
• Rank: $1$

Rank

The elliptic curve 864.e1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 864.e do not have complex multiplication.

Modular form 864.2.a.e

Elliptic curves in class 864.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
864.e1	864a1	\([0, 0, 0, -3, 6]\)	\(-216\)	\(-13824\)	\([]\)	\(48\)	\(-0.52078\)	\(\Gamma_0(N)\)-optimal