Elliptic curve isogeny class with LMFDB label 81120.m (Cremona label 81120e)

• Label: 81120.m
• Number of curves: $4$
• Conductor: $81120$
• CM: no
• Rank: $1$

Elliptic curves in class 81120.m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
81120.m1	81120e4	\([0, -1, 0, -81176, 8929140]\)	\(23937672968/45\)	\(111209679360\)	\([2]\)	\(294912\)	\(1.3748\)
81120.m2	81120e3	\([0, -1, 0, -13576, -423320]\)	\(111980168/32805\)	\(81071856253440\)	\([2]\)	\(294912\)	\(1.3748\)
81120.m3	81120e1	\([0, -1, 0, -5126, 137760]\)	\(48228544/2025\)	\(625554446400\)	\([2, 2]\)	\(147456\)	\(1.0282\)	\(\Gamma_0(N)\)-optimal
81120.m4	81120e2	\([0, -1, 0, 2479, 504321]\)	\(85184/5625\)	\(-111209679360000\)	\([2]\)	\(294912\)	\(1.3748\)

Rank

The elliptic curves in class 81120.m have rank \(1\).

Complex multiplication

The elliptic curves in class 81120.m do not have complex multiplication.

Modular form 81120.2.a.m

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.