Elliptic curve isogeny class with LMFDB label 550.b (Cremona label 550c)

• Label: 550.b
• Number of curves: $1$
• Conductor: $550$
• CM: no
• Rank: $0$

Rank

The elliptic curve 550.b1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 550.b do not have complex multiplication.

Modular form 550.2.a.b

Elliptic curves in class 550.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
550.b1	550c1	\([1, 0, 1, -206, -1152]\)	\(-38401771585/22528\)	\(-563200\)	\([]\)	\(132\)	\(0.048433\)	\(\Gamma_0(N)\)-optimal