Elliptic curve isogeny class with Cremona label 112554e (LMFDB label 112554.a)

• Label: 112554e
• Number of curves: $1$
• Conductor: $112554$
• CM: no
• Rank: $0$

Rank

The elliptic curve 112554e1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(13\)	\(1\)
\(37\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 112554e do not have complex multiplication.

Modular form 112554.2.a.e

Elliptic curves in class 112554e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
112554.a1	112554e1	\([1, -1, 0, -277304949, -1777342088651]\)	\(-670206957616537490521/6109179936768\)	\(-21496638787328774504448\)	\([]\)	\(44592768\)	\(3.4498\)	\(\Gamma_0(N)\)-optimal