Elliptic curve isogeny class with LMFDB label 2080.e (Cremona label 2080e)

• Label: 2080.e
• Number of curves: $4$
• Conductor: $2080$
• CM: no
• Rank: $0$

Elliptic curves in class 2080.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2080.e1	2080e3	\([0, 0, 0, -3467, 78574]\)	\(9001508089608/325\)	\(166400\)	\([4]\)	\(1024\)	\(0.49667\)
2080.e2	2080e2	\([0, 0, 0, -347, -414]\)	\(9024895368/5078125\)	\(2600000000\)	\([2]\)	\(1024\)	\(0.49667\)
2080.e3	2080e1	\([0, 0, 0, -217, 1224]\)	\(17657244864/105625\)	\(6760000\)	\([2, 2]\)	\(512\)	\(0.15009\)	\(\Gamma_0(N)\)-optimal
2080.e4	2080e4	\([0, 0, 0, -92, 2624]\)	\(-21024576/714025\)	\(-2924646400\)	\([4]\)	\(1024\)	\(0.49667\)

Rank

The elliptic curves in class 2080.e have rank \(0\).

Complex multiplication

The elliptic curves in class 2080.e do not have complex multiplication.

Modular form 2080.2.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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.