Elliptic curve isogeny class with LMFDB label 162624.e (Cremona label 162624cd)

• Label: 162624.e
• Number of curves: $1$
• Conductor: $162624$
• CM: no
• Rank: $1$

Rank

The elliptic curve 162624.e1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 162624.e do not have complex multiplication.

Modular form 162624.2.a.e

Elliptic curves in class 162624.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
162624.e1	162624cd1	\([0, -1, 0, -117, -339]\)	\(90112/21\)	\(41631744\)	\([]\)	\(36864\)	\(0.17399\)	\(\Gamma_0(N)\)-optimal