Elliptic curve isogeny class with Cremona label 484968m (LMFDB label 484968.m)

• Label: 484968m
• Number of curves: $2$
• Conductor: $484968$
• CM: no
• Rank: $1$

Elliptic curves in class 484968m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
484968.m2	484968m1	\([0, 1, 0, -32468, 3916416]\)	\(-8346562000/9861183\)	\(-4472239927465728\)	\([2]\)	\(2252800\)	\(1.6970\)	\(\Gamma_0(N)\)-optimal^*
484968.m1	484968m2	\([0, 1, 0, -620528, 187861584]\)	\(14566408766500/6777027\)	\(12294058730646528\)	\([2]\)	\(4505600\)	\(2.0436\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 484968m1.

Rank

The elliptic curves in class 484968m have rank \(1\).

Complex multiplication

The elliptic curves in class 484968m do not have complex multiplication.

Modular form 484968.2.a.m

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.