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

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

Elliptic curves in class 487872oc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
487872.oc4	487872oc1	\([0, 0, 0, -44920524, -38336271248]\)	\(29609739866953/15259926528\)	\(5166256965603919562539008\)	\([2]\)	\(88473600\)	\(3.4341\)	\(\Gamma_0(N)\)-optimal^*
487872.oc2	487872oc2	\([0, 0, 0, -401764044, 3072054586480]\)	\(21184262604460873/216872764416\)	\(73422400019954923235966976\)	\([2, 2]\)	\(176947200\)	\(3.7807\)	\(\Gamma_0(N)\)-optimal^*
487872.oc1	487872oc3	\([0, 0, 0, -6412347084, 197639436057712]\)	\(86129359107301290313/9166294368\)	\(3103254268004820213301248\)	\([2]\)	\(353894400\)	\(4.1273\)	\(\Gamma_0(N)\)-optimal^*
487872.oc3	487872oc4	\([0, 0, 0, -100677324, 7569688009840]\)	\(-333345918055753/72923718045024\)	\(-24688366986339495663699492864\)	\([2]\)	\(353894400\)	\(4.1273\)

^*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 487872oc1.

Rank

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

Complex multiplication

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

Modular form 487872.2.a.oc

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.