Elliptic curve isogeny class with LMFDB label 162240.cq (Cremona label 162240ci)

• Label: 162240.cq
• Number of curves: $1$
• Conductor: $162240$
• CM: no
• Rank: $1$

Rank

The elliptic curve 162240.cq1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 162240.cq do not have complex multiplication.

Modular form 162240.2.a.cq

Elliptic curves in class 162240.cq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162240.cq1	162240ci1	\([0, -1, 0, -459905, 749712417]\)	\(-50308609/1105920\)	\(-236488731910031278080\)	\([]\)	\(4672512\)	\(2.5902\)	\(\Gamma_0(N)\)-optimal