Elliptic curve isogeny class with Cremona label 32760p (LMFDB label 32760.y)

• Label: 32760p
• Number of curves: $4$
• Conductor: $32760$
• CM: no
• Rank: $1$

Elliptic curves in class 32760p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
32760.y4	32760p1	\([0, 0, 0, -57522, -2191439]\)	\(1804588288006144/866455078125\)	\(10106332031250000\)	\([4]\)	\(172032\)	\(1.7648\)	\(\Gamma_0(N)\)-optimal
32760.y2	32760p2	\([0, 0, 0, -760647, -255175814]\)	\(260798860029250384/196803140625\)	\(36728189316000000\)	\([2, 2]\)	\(344064\)	\(2.1113\)
32760.y3	32760p3	\([0, 0, 0, -603147, -363882314]\)	\(-32506165579682596/57814914850875\)	\(-43158602676518784000\)	\([2]\)	\(688128\)	\(2.4579\)
32760.y1	32760p4	\([0, 0, 0, -12168147, -16337469314]\)	\(266912903848829942596/152163375\)	\(113589350784000\)	\([2]\)	\(688128\)	\(2.4579\)

Rank

The elliptic curves in class 32760p have rank \(1\).

Complex multiplication

The elliptic curves in class 32760p do not have complex multiplication.

Modular form 32760.2.a.p

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.