Elliptic curve isogeny class with Cremona label 48510bf (LMFDB label 48510.y)

• Label: 48510bf
• Number of curves: $4$
• Conductor: $48510$
• CM: no
• Rank: $0$

Elliptic curves in class 48510bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48510.y3	48510bf1	\([1, -1, 0, -437040, -76538624]\)	\(107639597521009/32699842560\)	\(2804538653681909760\)	\([2]\)	\(983040\)	\(2.2448\)	\(\Gamma_0(N)\)-optimal
48510.y2	48510bf2	\([1, -1, 0, -2694960, 1644448000]\)	\(25238585142450289/995844326400\)	\(85409704995185894400\)	\([2, 2]\)	\(1966080\)	\(2.5914\)
48510.y4	48510bf3	\([1, -1, 0, 1185840, 5988615520]\)	\(2150235484224911/181905111732960\)	\(-15601295823407567048160\)	\([2]\)	\(3932160\)	\(2.9380\)
48510.y1	48510bf4	\([1, -1, 0, -42702480, 107416329376]\)	\(100407751863770656369/166028940000\)	\(14239658157541740000\)	\([2]\)	\(3932160\)	\(2.9380\)

Rank

The elliptic curves in class 48510bf have rank \(0\).

Complex multiplication

The elliptic curves in class 48510bf do not have complex multiplication.

Modular form 48510.2.a.bf

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.