Elliptic curve isogeny class with Cremona label 81120t (LMFDB label 81120.bd)

• Label: 81120t
• Number of curves: $4$
• Conductor: $81120$
• CM: no
• Rank: $2$

Elliptic curves in class 81120t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
81120.bd3	81120t1	\([0, 1, 0, -5126, -137760]\)	\(48228544/2025\)	\(625554446400\)	\([2, 2]\)	\(147456\)	\(1.0282\)	\(\Gamma_0(N)\)-optimal
81120.bd4	81120t2	\([0, 1, 0, 2479, -504321]\)	\(85184/5625\)	\(-111209679360000\)	\([2]\)	\(294912\)	\(1.3748\)
81120.bd2	81120t3	\([0, 1, 0, -13576, 423320]\)	\(111980168/32805\)	\(81071856253440\)	\([2]\)	\(294912\)	\(1.3748\)
81120.bd1	81120t4	\([0, 1, 0, -81176, -8929140]\)	\(23937672968/45\)	\(111209679360\)	\([2]\)	\(294912\)	\(1.3748\)

Rank

The elliptic curves in class 81120t have rank \(2\).

Complex multiplication

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

Modular form 81120.2.a.t

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.