Elliptic curve isogeny class with LMFDB label 286650.s (Cremona label 286650s)

• Label: 286650.s
• Number of curves: $1$
• Conductor: $286650$
• CM: no
• Rank: $1$

Rank

The elliptic curve 286650.s1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 5 T + 23 T^{2}\)	1.23.af
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 286650.s do not have complex multiplication.

Modular form 286650.2.a.s

Elliptic curves in class 286650.s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
286650.s1	286650s1	\([1, -1, 0, 100833, 34881741]\)	\(2284322013/11927552\)	\(-592002238464000000\)	\([]\)	\(3655680\)	\(2.0923\)	\(\Gamma_0(N)\)-optimal