Elliptic curve isogeny class with Cremona label 6336cm (LMFDB label 6336.i)

• Label: 6336cm
• Number of curves: $2$
• Conductor: $6336$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 6336cm 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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6336cm do not have complex multiplication.

Modular form 6336.2.a.cm

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 6336cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6336.i2	6336cm1	\([0, 0, 0, 96, -416]\)	\(8192/11\)	\(-131383296\)	\([]\)	\(1920\)	\(0.24359\)	\(\Gamma_0(N)\)-optimal
6336.i1	6336cm2	\([0, 0, 0, -2784, -56864]\)	\(-199794688/1331\)	\(-15897378816\)	\([]\)	\(5760\)	\(0.79289\)