Elliptic curve isogeny class with LMFDB label 228672.cl (Cremona label 228672cs)

• Label: 228672.cl
• Number of curves: $1$
• Conductor: $228672$
• CM: no
• Rank: $1$

Rank

The elliptic curve 228672.cl1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(397\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 228672.cl do not have complex multiplication.

Modular form 228672.2.a.cl

Isogeny graph

Elliptic curves in class 228672.cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
228672.cl1	228672cs1	\([0, 0, 0, -1227, 16508]\)	\(4378747456/10719\)	\(500105664\)	\([]\)	\(92160\)	\(0.54747\)	\(\Gamma_0(N)\)-optimal