Elliptic curve isogeny class with LMFDB label 57498.s (Cremona label 57498s)

• Label: 57498.s
• Number of curves: $1$
• Conductor: $57498$
• CM: no
• Rank: $0$

Rank

The elliptic curve 57498.s1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(7\)	\(1 - T\)
\(37\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 57498.s do not have complex multiplication.

Modular form 57498.2.a.s

Elliptic curves in class 57498.s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
57498.s1	57498s1	\([1, 0, 0, -865921, 310074107]\)	\(-27986475935881/76146\)	\(-195369803139714\)	\([]\)	\(984960\)	\(1.9759\)	\(\Gamma_0(N)\)-optimal