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 \(0\).

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.