Elliptic curve isogeny class with LMFDB label 162288.ek (Cremona label 162288dx)

• Label: 162288.ek
• Number of curves: $1$
• Conductor: $162288$
• CM: no
• Rank: $1$

Rank

The elliptic curve 162288.ek1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 162288.ek do not have complex multiplication.

Modular form 162288.2.a.ek

Elliptic curves in class 162288.ek

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162288.ek1	162288dx1	\([0, 0, 0, 73652733, -183848983038]\)	\(13581780628779/12348030976\)	\(-40172726758608531017957376\)	\([]\)	\(26191872\)	\(3.6003\)	\(\Gamma_0(N)\)-optimal