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

• Label: 486720.jh
• Number of curves: $4$
• Conductor: $486720$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 486720.jh have rank \(1\).

Complex multiplication

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

Modular form 486720.2.a.jh

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 486720.jh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
486720.jh1	486720jh4	\([0, 0, 0, -48933612, -78917048496]\)	\(520300455507/193072360\)	\(4808520074168039091732480\)	\([2]\)	\(111476736\)	\(3.4360\)	\(\Gamma_0(N)\)-optimal^*
486720.jh2	486720jh2	\([0, 0, 0, -43255212, -109497882416]\)	\(261984288445803/42250\)	\(1443412670349312000\)	\([2]\)	\(37158912\)	\(2.8867\)	\(\Gamma_0(N)\)-optimal^*
486720.jh3	486720jh1	\([0, 0, 0, -2695212, -1721850416]\)	\(-63378025803/812500\)	\(-27757935968256000000\)	\([2]\)	\(18579456\)	\(2.5401\)	\(\Gamma_0(N)\)-optimal^*
486720.jh4	486720jh3	\([0, 0, 0, 9472788, -8759280816]\)	\(3774555693/3515200\)	\(-87547020012162750873600\)	\([2]\)	\(55738368\)	\(3.0894\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 486720.jh1.