Elliptic curve isogeny class with LMFDB label 11760.cl (Cremona label 11760co)

• Label: 11760.cl
• Number of curves: $8$
• Conductor: $11760$
• CM: no
• Rank: $1$

Elliptic curves in class 11760.cl

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
11760.cl1	11760co7	[0, 1, 0, -5057600, 2752600500]	[2]	663552
11760.cl2	11760co4	[0, 1, 0, -4516640, 3693127668]	[2]	221184
11760.cl3	11760co6	[0, 1, 0, -2117600, -1155247500]	[2, 2]	331776
11760.cl4	11760co3	[0, 1, 0, -2101920, -1173630732]	[2]	165888
11760.cl5	11760co2	[0, 1, 0, -283040, 57311988]	[2, 2]	110592
11760.cl6	11760co5	[0, 1, 0, -63520, 144154100]	[4]	221184
11760.cl7	11760co1	[0, 1, 0, -32160, -791820]	[2]	55296	\(\Gamma_0(N)\)-optimal
11760.cl8	11760co8	[0, 1, 0, 571520, -3886317772]	[4]	663552

Rank

The elliptic curves in class 11760.cl have rank \(1\).

Complex multiplication

The elliptic curves in class 11760.cl do not have complex multiplication.

Modular form 11760.2.a.cl

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.