Elliptic curve isogeny class with Cremona label 270480fz (LMFDB label 270480.fz)

• Label: 270480fz
• Number of curves: $4$
• Conductor: $270480$
• CM: no
• Rank: $1$

Elliptic curves in class 270480fz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
270480.fz3	270480fz1	\([0, 1, 0, -219536, 39403860]\)	\(2428257525121/8150625\)	\(3927707159040000\)	\([2]\)	\(1572864\)	\(1.8565\)	\(\Gamma_0(N)\)-optimal
270480.fz2	270480fz2	\([0, 1, 0, -317536, 635060]\)	\(7347774183121/4251692025\)	\(2048849162441625600\)	\([2, 2]\)	\(3145728\)	\(2.2031\)
270480.fz4	270480fz3	\([0, 1, 0, 1270064, 6350420]\)	\(470166844956479/272118787605\)	\(-131131405283084881920\)	\([2]\)	\(6291456\)	\(2.5497\)
270480.fz1	270480fz4	\([0, 1, 0, -3473136, -2484715500]\)	\(9614816895690721/34652610405\)	\(16698756962459013120\)	\([2]\)	\(6291456\)	\(2.5497\)

Rank

The elliptic curves in class 270480fz have rank \(1\).

Complex multiplication

The elliptic curves in class 270480fz do not have complex multiplication.

Modular form 270480.2.a.fz

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.