Elliptic curve isogeny class with LMFDB label 384678.bn (Cremona label 384678bn)

• Label: 384678.bn
• Number of curves: $1$
• Conductor: $384678$
• CM: no
• Rank: $0$

Rank

The elliptic curve 384678.bn1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(43\)	\(1 + T\)
\(71\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 384678.bn do not have complex multiplication.

Modular form 384678.2.a.bn

Elliptic curves in class 384678.bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
384678.bn1	384678bn1	\([1, -1, 1, -212, 1237]\)	\(38854881603/42742\)	\(1154034\)	\([]\)	\(96768\)	\(0.078170\)	\(\Gamma_0(N)\)-optimal