Elliptic curve isogeny class with LMFDB label 6720.ck (Cremona label 6720cl)

• Label: 6720.ck
• Number of curves: $4$
• Conductor: $6720$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 6720.ck have rank \(1\).

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
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 6720.2.a.ck

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 6720.ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6720.ck1	6720cl3	\([0, 1, 0, -810465, -272909025]\)	\(898353183174324196/29899176238575\)	\(1959472413971251200\)	\([2]\)	\(122880\)	\(2.2828\)
6720.ck2	6720cl2	\([0, 1, 0, -124465, 10957775]\)	\(13015144447800784/4341909875625\)	\(71137851402240000\)	\([2, 2]\)	\(61440\)	\(1.9362\)
6720.ck3	6720cl1	\([0, 1, 0, -111965, 14380275]\)	\(151591373397612544/32558203125\)	\(33339600000000\)	\([2]\)	\(30720\)	\(1.5897\)	\(\Gamma_0(N)\)-optimal
6720.ck4	6720cl4	\([0, 1, 0, 361535, 75984575]\)	\(79743193254623804/84085819746075\)	\(-5510648282878771200\)	\([2]\)	\(122880\)	\(2.2828\)