Elliptic curve isogeny class with LMFDB label 6336.bf (Cremona label 6336ce)

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

Rank

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

See L-function page for more information

Complex multiplication

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

Modular form 6336.2.a.bf

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 6336.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6336.bf1	6336ce3	\([0, 0, 0, -46380, -3829808]\)	\(57736239625/255552\)	\(48836747722752\)	\([2]\)	\(18432\)	\(1.4790\)
6336.bf2	6336ce4	\([0, 0, 0, -23340, -7636016]\)	\(-7357983625/127552392\)	\(-24375641707118592\)	\([2]\)	\(36864\)	\(1.8255\)
6336.bf3	6336ce1	\([0, 0, 0, -3180, 65104]\)	\(18609625/1188\)	\(227030335488\)	\([2]\)	\(6144\)	\(0.92964\)	\(\Gamma_0(N)\)-optimal
6336.bf4	6336ce2	\([0, 0, 0, 2580, 274768]\)	\(9938375/176418\)	\(-33714004819968\)	\([2]\)	\(12288\)	\(1.2762\)