Elliptic curve isogeny class with LMFDB label 339864.cx (Cremona label 339864cx)

• Label: 339864.cx
• Number of curves: $1$
• Conductor: $339864$
• CM: no
• Rank: $1$

Rank

The elliptic curve 339864.cx1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 339864.cx do not have complex multiplication.

Modular form 339864.2.a.cx

Elliptic curves in class 339864.cx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
339864.cx1	339864cx1	\([0, 1, 0, -4342984, 3488117744]\)	\(-130098552670514/257298363\)	\(-17916495229709604864\)	\([]\)	\(10450944\)	\(2.5824\)	\(\Gamma_0(N)\)-optimal