Elliptic curve isogeny class with LMFDB label 6720.cc (Cremona label 6720cg)

• Label: 6720.cc
• Number of curves: $8$
• Conductor: $6720$
• CM: no
• Rank: $0$

Elliptic curves in class 6720.cc

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
6720.cc1	6720cg7	[0, 1, 0, -412865, -64377537]	[2]	110592
6720.cc2	6720cg4	[0, 1, 0, -368705, -86295105]	[2]	36864
6720.cc3	6720cg6	[0, 1, 0, -172865, 26870463]	[2, 2]	55296
6720.cc4	6720cg3	[0, 1, 0, -171585, 27299775]	[2]	27648
6720.cc5	6720cg2	[0, 1, 0, -23105, -1346625]	[2, 2]	18432
6720.cc6	6720cg5	[0, 1, 0, -5185, -3364417]	[4]	36864
6720.cc7	6720cg1	[0, 1, 0, -2625, 17343]	[2]	9216	\(\Gamma_0(N)\)-optimal
6720.cc8	6720cg8	[0, 1, 0, 46655, 90662975]	[4]	110592

Rank

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

Complex multiplication

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

Modular form 6720.2.a.cc

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.