Elliptic curve isogeny class with Cremona label 87120fy (LMFDB label 87120.fp)

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

Elliptic curves in class 87120fy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
87120.fp4	87120fy1	\([0, 0, 0, 238128, 164337239]\)	\(72268906496/606436875\)	\(-12531100788527310000\)	\([2]\)	\(1105920\)	\(2.3459\)	\(\Gamma_0(N)\)-optimal
87120.fp3	87120fy2	\([0, 0, 0, -3437247, 2258565914]\)	\(13584145739344/1195803675\)	\(395351588729596435200\)	\([2]\)	\(2211840\)	\(2.6925\)
87120.fp2	87120fy3	\([0, 0, 0, -17011632, 27027819731]\)	\(-26348629355659264/24169921875\)	\(-499434878636718750000\)	\([2]\)	\(3317760\)	\(2.8952\)
87120.fp1	87120fy4	\([0, 0, 0, -272246007, 1728981679106]\)	\(6749703004355978704/5671875\)	\(1875211490988000000\)	\([2]\)	\(6635520\)	\(3.2418\)

Rank

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

Complex multiplication

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

Modular form 87120.2.a.fy

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.