Elliptic curve isogeny class with LMFDB label 6336.cj (Cremona label 6336ci)

• Label: 6336.cj
• Number of curves: $4$
• Conductor: $6336$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 6336.cj have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	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 6336.cj do not have complex multiplication.

Modular form 6336.2.a.cj

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 LMFDB 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 LMFDB labels.

Elliptic curves in class 6336.cj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6336.cj1	6336ci3	\([0, 0, 0, -202764, -35142640]\)	\(4824238966273/66\)	\(12612796416\)	\([2]\)	\(24576\)	\(1.4941\)
6336.cj2	6336ci2	\([0, 0, 0, -12684, -548080]\)	\(1180932193/4356\)	\(832444563456\)	\([2, 2]\)	\(12288\)	\(1.1475\)
6336.cj3	6336ci4	\([0, 0, 0, -6924, -1048048]\)	\(-192100033/2371842\)	\(-453266064801792\)	\([2]\)	\(24576\)	\(1.4941\)
6336.cj4	6336ci1	\([0, 0, 0, -1164, 272]\)	\(912673/528\)	\(100902371328\)	\([2]\)	\(6144\)	\(0.80093\)	\(\Gamma_0(N)\)-optimal