Elliptic curve isogeny class with Cremona label 486720op (LMFDB label 486720.op)

• Label: 486720op
• Number of curves: $4$
• Conductor: $486720$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 486720op have rank \(0\).

Complex multiplication

The elliptic curves in class 486720op do not have complex multiplication.

Modular form 486720.2.a.op

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 486720op

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
486720.op3	486720op1	\([0, 0, 0, -586092, 1108588624]\)	\(-24137569/561600\)	\(-518029704213980774400\)	\([2]\)	\(12386304\)	\(2.6554\)	\(\Gamma_0(N)\)-optimal^*
486720.op2	486720op2	\([0, 0, 0, -20054892, 34415811664]\)	\(967068262369/4928040\)	\(4545710654477681295360\)	\([2]\)	\(24772608\)	\(3.0020\)	\(\Gamma_0(N)\)-optimal^*
486720.op4	486720op3	\([0, 0, 0, 5254548, -29293110704]\)	\(17394111071/411937500\)	\(-379978385469456384000000\)	\([2]\)	\(37158912\)	\(3.2048\)
486720.op1	486720op4	\([0, 0, 0, -116425452, -458920854704]\)	\(189208196468929/10860320250\)	\(10017750154516748107776000\)	\([2]\)	\(74317824\)	\(3.5513\)

^*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 486720op1.