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

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

Elliptic curves in class 486720qh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
486720.qh3	486720qh1	\([0, 0, 0, -2695212, 1721850416]\)	\(-63378025803/812500\)	\(-27757935968256000000\)	\([2]\)	\(18579456\)	\(2.5401\)	\(\Gamma_0(N)\)-optimal^*
486720.qh2	486720qh2	\([0, 0, 0, -43255212, 109497882416]\)	\(261984288445803/42250\)	\(1443412670349312000\)	\([2]\)	\(37158912\)	\(2.8867\)	\(\Gamma_0(N)\)-optimal^*
486720.qh4	486720qh3	\([0, 0, 0, 9472788, 8759280816]\)	\(3774555693/3515200\)	\(-87547020012162750873600\)	\([2]\)	\(55738368\)	\(3.0894\)
486720.qh1	486720qh4	\([0, 0, 0, -48933612, 78917048496]\)	\(520300455507/193072360\)	\(4808520074168039091732480\)	\([2]\)	\(111476736\)	\(3.4360\)

^*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 486720qh1.

Rank

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

Complex multiplication

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

Modular form 486720.2.a.qh

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.