Elliptic curve isogeny class with LMFDB label 87120.fn (Cremona label 87120fz)

• Label: 87120.fn
• Number of curves: $4$
• Conductor: $87120$
• CM: no
• Rank: $1$

Elliptic curves in class 87120.fn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
87120.fn1	87120fz3	\([0, 0, 0, -45012, 3674891]\)	\(488095744/125\)	\(2582935938000\)	\([2]\)	\(207360\)	\(1.3676\)
87120.fn2	87120fz4	\([0, 0, 0, -39567, 4597274]\)	\(-20720464/15625\)	\(-5165871876000000\)	\([2]\)	\(414720\)	\(1.7142\)
87120.fn3	87120fz1	\([0, 0, 0, -1452, -14641]\)	\(16384/5\)	\(103317437520\)	\([2]\)	\(69120\)	\(0.81830\)	\(\Gamma_0(N)\)-optimal
87120.fn4	87120fz2	\([0, 0, 0, 3993, -98494]\)	\(21296/25\)	\(-8265395001600\)	\([2]\)	\(138240\)	\(1.1649\)

Rank

The elliptic curves in class 87120.fn have rank \(1\).

Complex multiplication

The elliptic curves in class 87120.fn do not have complex multiplication.

Modular form 87120.2.a.fn

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.