Elliptic curve isogeny class with Cremona label 1560c (LMFDB label 1560.i)

• Label: 1560c
• Number of curves: $4$
• Conductor: $1560$
• CM: no
• Rank: $0$

Elliptic curves in class 1560c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1560.i3	1560c1	\([0, 1, 0, -4876, 129440]\)	\(50091484483024/14625\)	\(3744000\)	\([2]\)	\(768\)	\(0.62742\)	\(\Gamma_0(N)\)-optimal
1560.i2	1560c2	\([0, 1, 0, -4896, 128304]\)	\(12677589459076/213890625\)	\(219024000000\)	\([2, 2]\)	\(1536\)	\(0.97399\)
1560.i1	1560c3	\([0, 1, 0, -9896, -183696]\)	\(52337949619538/23423590125\)	\(47971512576000\)	\([2]\)	\(3072\)	\(1.3206\)
1560.i4	1560c4	\([0, 1, 0, -216, 367920]\)	\(-546718898/28564453125\)	\(-58500000000000\)	\([2]\)	\(3072\)	\(1.3206\)

Rank

The elliptic curves in class 1560c have rank \(0\).

Complex multiplication

The elliptic curves in class 1560c do not have complex multiplication.

Modular form 1560.2.a.c

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 Cremona 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 Cremona labels.