Elliptic curve isogeny class with LMFDB label 474320.bj (Cremona label 474320bj)

• Label: 474320.bj
• Number of curves: $4$
• Conductor: $474320$
• CM: no
• Rank: $1$

Elliptic curves in class 474320.bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
474320.bj1	474320bj4	\([0, 1, 0, -2477470200, 46117850491348]\)	\(1969902499564819009/63690429687500\)	\(54372396828097964000000000000\)	\([2]\)	\(477757440\)	\(4.2877\)	\(\Gamma_0(N)\)-optimal^*
474320.bj2	474320bj2	\([0, 1, 0, -339235640, -2383668253100]\)	\(5057359576472449/51765560000\)	\(44192158604656373104640000\)	\([2]\)	\(159252480\)	\(3.7384\)	\(\Gamma_0(N)\)-optimal^*
474320.bj3	474320bj1	\([0, 1, 0, -5314360, -91766155692]\)	\(-19443408769/4249907200\)	\(-3628137569408523226316800\)	\([2]\)	\(79626240\)	\(3.3918\)	\(\Gamma_0(N)\)-optimal^*
474320.bj4	474320bj3	\([0, 1, 0, 47809480, 2471926614100]\)	\(14156681599871/3100231750000\)	\(-2646661857945541123072000000\)	\([2]\)	\(238878720\)	\(3.9411\)	\(\Gamma_0(N)\)-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 474320.bj1.

Rank

The elliptic curves in class 474320.bj have rank \(1\).

Complex multiplication

The elliptic curves in class 474320.bj do not have complex multiplication.

Modular form 474320.2.a.bj

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.