Elliptic curve isogeny class with LMFDB label 118.b (Cremona label 118d)

• Label: 118.b
• Number of curves: $1$
• Conductor: $118$
• CM: no
• Rank: $0$

Rank

The elliptic curve 118.b1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(59\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 118.b do not have complex multiplication.

Modular form 118.2.a.b

Isogeny graph

Elliptic curves in class 118.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
118.b1	118d1	\([1, 1, 0, 56, -192]\)	\(18884848247/30932992\)	\(-30932992\)	\([]\)	\(38\)	\(0.12237\)	\(\Gamma_0(N)\)-optimal