Elliptic curve isogeny class with LMFDB label 388416.bn (Cremona label 388416bn)

• Label: 388416.bn
• Number of curves: $1$
• Conductor: $388416$
• CM: no
• Rank: $1$

Rank

The elliptic curve 388416.bn1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 388416.bn do not have complex multiplication.

Modular form 388416.2.a.bn

Elliptic curves in class 388416.bn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388416.bn1	388416bn1	\([0, -1, 0, -109960261, 443851522909]\)	\(-371806976516936704/89266779\)	\(-35302326886731792384\)	\([]\)	\(24772608\)	\(3.1288\)	\(\Gamma_0(N)\)-optimal