Elliptic curve isogeny class with LMFDB label 88752.e (Cremona label 88752k)

• Label: 88752.e
• Number of curves: $1$
• Conductor: $88752$
• CM: no
• Rank: $0$

Rank

The elliptic curve 88752.e1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(43\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 88752.e do not have complex multiplication.

Modular form 88752.2.a.e

Elliptic curves in class 88752.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
88752.e1	88752k1	\([0, -1, 0, 1404624, 38733534144]\)	\(148877/314928\)	\(-648316871033020794077184\)	\([]\)	\(6538752\)	\(3.2480\)	\(\Gamma_0(N)\)-optimal