Elliptic curve isogeny class with LMFDB label 52800.ct (Cremona label 52800br)

• Label: 52800.ct
• Number of curves: $1$
• Conductor: $52800$
• CM: no
• Rank: $1$

Rank

The elliptic curve 52800.ct1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 52800.ct do not have complex multiplication.

Modular form 52800.2.a.ct

Elliptic curves in class 52800.ct

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
52800.ct1	52800br1	\([0, -1, 0, 3167, -4378463]\)	\(137180/323433\)	\(-8279884800000000\)	\([]\)	\(230400\)	\(1.7333\)	\(\Gamma_0(N)\)-optimal