Elliptic curve isogeny class with Cremona label 6336g (LMFDB label 6336.bm)

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

Rank

The elliptic curves in class 6336g 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 8 T + 17 T^{2}\)	1.17.ai
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 6336.2.a.g

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 6336g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6336.bm4	6336g1	\([0, 0, 0, -4140, 98864]\)	\(1108717875/45056\)	\(318901321728\)	\([2]\)	\(6144\)	\(0.97321\)	\(\Gamma_0(N)\)-optimal
6336.bm2	6336g2	\([0, 0, 0, -65580, 6464048]\)	\(4406910829875/7744\)	\(54811164672\)	\([2]\)	\(12288\)	\(1.3198\)
6336.bm3	6336g3	\([0, 0, 0, -50220, -4302288]\)	\(2714704875/21296\)	\(109882682376192\)	\([2]\)	\(18432\)	\(1.5225\)
6336.bm1	6336g4	\([0, 0, 0, -84780, 2374704]\)	\(13060888875/7086244\)	\(36563462560677888\)	\([2]\)	\(36864\)	\(1.8691\)