Elliptic curve isogeny class with Cremona label 6720bc (LMFDB label 6720.cm)

• Label: 6720bc
• Number of curves: $4$
• Conductor: $6720$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 6720bc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6720bc do not have complex multiplication.

Modular form 6720.2.a.bc

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 6720bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6720.cm4	6720bc1	\([0, 1, 0, 35, -637]\)	\(4499456/180075\)	\(-184396800\)	\([2]\)	\(2048\)	\(0.26590\)	\(\Gamma_0(N)\)-optimal
6720.cm3	6720bc2	\([0, 1, 0, -945, -11025]\)	\(5702413264/275625\)	\(4515840000\)	\([2, 2]\)	\(4096\)	\(0.61247\)
6720.cm1	6720bc3	\([0, 1, 0, -14945, -708225]\)	\(5633270409316/14175\)	\(928972800\)	\([2]\)	\(8192\)	\(0.95905\)
6720.cm2	6720bc4	\([0, 1, 0, -2625, 37023]\)	\(30534944836/8203125\)	\(537600000000\)	\([2]\)	\(8192\)	\(0.95905\)