Elliptic curve isogeny class with Cremona label 113288u (LMFDB label 113288.n)

• Label: 113288u
• Number of curves: $1$
• Conductor: $113288$
• CM: no
• Rank: $1$

Rank

The elliptic curve 113288u1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 113288u do not have complex multiplication.

Modular form 113288.2.a.u

Elliptic curves in class 113288u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
113288.n1	113288u1	\([0, 0, 0, -74246123, 246562353926]\)	\(-3241463778/4913\)	\(-68604190600952468998144\)	\([]\)	\(11031552\)	\(3.2820\)	\(\Gamma_0(N)\)-optimal