Elliptic curve isogeny class with Cremona label 270480e (LMFDB label 270480.e)

• Label: 270480e
• Number of curves: $4$
• Conductor: $270480$
• CM: no
• Rank: $1$

Elliptic curves in class 270480e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
270480.e3	270480e1	\([0, -1, 0, -55631, 5068050]\)	\(10115186538496/2113125\)	\(3977712690000\)	\([2]\)	\(1277952\)	\(1.4139\)	\(\Gamma_0(N)\)-optimal
270480.e2	270480e2	\([0, -1, 0, -61756, 3889600]\)	\(864848456656/285779025\)	\(8607133827129600\)	\([2, 2]\)	\(2555904\)	\(1.7605\)
270480.e4	270480e3	\([0, -1, 0, 178344, 26555040]\)	\(5207251926236/5553444645\)	\(-669037782056555520\)	\([2]\)	\(5111808\)	\(2.1070\)
270480.e1	270480e4	\([0, -1, 0, -399856, -94294640]\)	\(58687749106564/1988856345\)	\(239602647176094720\)	\([2]\)	\(5111808\)	\(2.1070\)

Rank

The elliptic curves in class 270480e have rank \(1\).

Complex multiplication

The elliptic curves in class 270480e do not have complex multiplication.

Modular form 270480.2.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.