Elliptic curve isogeny class with LMFDB label 47775.w (Cremona label 47775u)

• Label: 47775.w
• Number of curves: $4$
• Conductor: $47775$
• CM: no
• Rank: $1$

Elliptic curves in class 47775.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
47775.w1	47775u4	\([1, 1, 1, -85163, 9530156]\)	\(37159393753/1053\)	\(1935693703125\)	\([2]\)	\(147456\)	\(1.4593\)
47775.w2	47775u3	\([1, 1, 1, -23913, -1298844]\)	\(822656953/85683\)	\(157508113546875\)	\([2]\)	\(147456\)	\(1.4593\)
47775.w3	47775u2	\([1, 1, 1, -5538, 134406]\)	\(10218313/1521\)	\(2796002015625\)	\([2, 2]\)	\(73728\)	\(1.1127\)
47775.w4	47775u1	\([1, 1, 1, 587, 11906]\)	\(12167/39\)	\(-71692359375\)	\([2]\)	\(36864\)	\(0.76616\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 47775.w have rank \(1\).

Complex multiplication

The elliptic curves in class 47775.w do not have complex multiplication.

Modular form 47775.2.a.w

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.