Elliptic curve isogeny class with Cremona label 52800gr (LMFDB label 52800.fr)

• Label: 52800gr
• Number of curves: $4$
• Conductor: $52800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 52800gr have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 52800.2.a.gr

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 52800gr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
52800.fr3	52800gr1	\([0, 1, 0, -1233, 15663]\)	\(810448/33\)	\(8448000000\)	\([2]\)	\(32768\)	\(0.67056\)	\(\Gamma_0(N)\)-optimal
52800.fr2	52800gr2	\([0, 1, 0, -3233, -50337]\)	\(3650692/1089\)	\(1115136000000\)	\([2, 2]\)	\(65536\)	\(1.0171\)
52800.fr4	52800gr3	\([0, 1, 0, 8767, -326337]\)	\(36382894/43923\)	\(-89954304000000\)	\([2]\)	\(131072\)	\(1.3637\)
52800.fr1	52800gr4	\([0, 1, 0, -47233, -3966337]\)	\(5690357426/891\)	\(1824768000000\)	\([2]\)	\(131072\)	\(1.3637\)