Elliptic curve isogeny class with LMFDB label 228.a (Cremona label 228b)

• Label: 228.a
• Number of curves: $1$
• Conductor: $228$
• CM: no
• Rank: $1$

Rank

The elliptic curve 228.a1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 228.a do not have complex multiplication.

Modular form 228.2.a.a

Elliptic curves in class 228.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
228.a1	228b1	\([0, -1, 0, 3, 9]\)	\(8192/171\)	\(-43776\)	\([]\)	\(24\)	\(-0.42911\)	\(\Gamma_0(N)\)-optimal