Elliptic curve isogeny class with LMFDB label 61347.u (Cremona label 61347k)

• Label: 61347.u
• Number of curves: $4$
• Conductor: $61347$
• CM: no
• Rank: $0$

Elliptic curves in class 61347.u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
61347.u1	61347k4	\([1, 1, 0, -1421631, 651813804]\)	\(37159393753/1053\)	\(9004188867527997\)	\([2]\)	\(860160\)	\(2.1631\)
61347.u2	61347k3	\([1, 1, 0, -399181, -88071914]\)	\(822656953/85683\)	\(732674183035518867\)	\([2]\)	\(860160\)	\(2.1631\)
61347.u3	61347k2	\([1, 1, 0, -92446, 9285775]\)	\(10218313/1521\)	\(13006050586429329\)	\([2, 2]\)	\(430080\)	\(1.8165\)
61347.u4	61347k1	\([1, 1, 0, 9799, 799440]\)	\(12167/39\)	\(-333488476575111\)	\([2]\)	\(215040\)	\(1.4699\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 61347.u have rank \(0\).

Complex multiplication

The elliptic curves in class 61347.u do not have complex multiplication.

Modular form 61347.2.a.u

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.