Elliptic curve isogeny class with Cremona label 481650by (LMFDB label 481650.by)

• Label: 481650by
• Number of curves: $4$
• Conductor: $481650$
• CM: no
• Rank: $0$

Elliptic curves in class 481650by

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
481650.by4	481650by1	\([1, 1, 0, 15533125, -141414451875]\)	\(5495662324535111/117739817533440\)	\(-8879806420761968640000000\)	\([2]\)	\(123863040\)	\(3.4675\)	\(\Gamma_0(N)\)-optimal^*
481650.by3	481650by2	\([1, 1, 0, -330578875, -2191435827875]\)	\(52974743974734147769/3152005008998400\)	\(237720721023102470400000000\)	\([2, 2]\)	\(247726080\)	\(3.8140\)	\(\Gamma_0(N)\)-optimal^*
481650.by2	481650by3	\([1, 1, 0, -987650875, 9223876028125]\)	\(1412712966892699019449/330160465517040000\)	\(24900336037528723833750000000\)	\([2]\)	\(495452160\)	\(4.1606\)	\(\Gamma_0(N)\)-optimal^*
481650.by1	481650by4	\([1, 1, 0, -5211298875, -144801193507875]\)	\(207530301091125281552569/805586668007040\)	\(60756452803381136490000000\)	\([2]\)	\(495452160\)	\(4.1606\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 481650by1.

Rank

The elliptic curves in class 481650by have rank \(0\).

Complex multiplication

The elliptic curves in class 481650by do not have complex multiplication.

Modular form 481650.2.a.by

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.