Elliptic curve isogeny class with LMFDB label 487872.nr (Cremona label 487872nr)

• Label: 487872.nr
• Number of curves: $4$
• Conductor: $487872$
• CM: no
• Rank: $0$

Elliptic curves in class 487872.nr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
487872.nr1	487872nr3	\([0, 0, 0, -2805056364, 57182152499120]\)	\(7209828390823479793/49509306\)	\(16761404225334677078016\)	\([2]\)	\(141557760\)	\(3.8642\)	\(\Gamma_0(N)\)-optimal^*
487872.nr2	487872nr4	\([0, 0, 0, -244425324, 125104480688]\)	\(4770223741048753/2740574865798\)	\(927823208336481484606537728\)	\([2]\)	\(141557760\)	\(3.8642\)
487872.nr3	487872nr2	\([0, 0, 0, -175426284, 892291006640]\)	\(1763535241378513/4612311396\)	\(1561500694868833002848256\)	\([2, 2]\)	\(70778880\)	\(3.5176\)	\(\Gamma_0(N)\)-optimal^*
487872.nr4	487872nr1	\([0, 0, 0, -6761964, 24749210288]\)	\(-100999381393/723148272\)	\(-244822266380471387553792\)	\([2]\)	\(35389440\)	\(3.1711\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 487872.nr1.

Rank

The elliptic curves in class 487872.nr have rank \(0\).

Complex multiplication

The elliptic curves in class 487872.nr do not have complex multiplication.

Modular form 487872.2.a.nr

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.