Elliptic curve isogeny class with Cremona label 40560e (LMFDB label 40560.n)

• Label: 40560e
• Number of curves: $4$
• Conductor: $40560$
• CM: no
• Rank: $1$

Elliptic curves in class 40560e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40560.n4	40560e1	\([0, -1, 0, -387911, 78529086]\)	\(83587439220736/13990184325\)	\(1080447161785102800\)	\([2]\)	\(516096\)	\(2.1814\)	\(\Gamma_0(N)\)-optimal
40560.n2	40560e2	\([0, -1, 0, -5931956, 5562698400]\)	\(18681746265374416/693005625\)	\(856321481676960000\)	\([2, 2]\)	\(1032192\)	\(2.5280\)
40560.n3	40560e3	\([0, -1, 0, -5658176, 6099088176]\)	\(-4053153720264484/903687890625\)	\(-4466615135907600000000\)	\([2]\)	\(2064384\)	\(2.8746\)
40560.n1	40560e4	\([0, -1, 0, -94910456, 355924440000]\)	\(19129597231400697604/26325\)	\(130115324851200\)	\([4]\)	\(2064384\)	\(2.8746\)

Rank

The elliptic curves in class 40560e have rank \(1\).

Complex multiplication

The elliptic curves in class 40560e do not have complex multiplication.

Modular form 40560.2.a.e

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.