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 \(1\).

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.