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

• Label: 474320bd
• Number of curves: $4$
• Conductor: $474320$
• CM: no
• Rank: $0$

Elliptic curves in class 474320bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
474320.bd4	474320bd1	\([0, 1, 0, 946664, -2897181036]\)	\(109902239/4312000\)	\(-3681146072857673728000\)	\([2]\)	\(26542080\)	\(2.8180\)	\(\Gamma_0(N)\)-optimal^*
474320.bd2	474320bd2	\([0, 1, 0, -25615256, -47765576300]\)	\(2177286259681/105875000\)	\(90385283038916096000000\)	\([2]\)	\(53084160\)	\(3.1646\)	\(\Gamma_0(N)\)-optimal^*
474320.bd3	474320bd3	\([0, 1, 0, -8539736, 79251248404]\)	\(-80677568161/3131816380\)	\(-2673625595581710572830720\)	\([2]\)	\(79626240\)	\(3.3673\)	\(\Gamma_0(N)\)-optimal^*
474320.bd1	474320bd4	\([0, 1, 0, -333923256, 2335720882900]\)	\(4823468134087681/30382271150\)	\(25937286207866303006105600\)	\([2]\)	\(159252480\)	\(3.7139\)	\(\Gamma_0(N)\)-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 474320bd1.

Rank

The elliptic curves in class 474320bd have rank \(0\).

Complex multiplication

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

Modular form 474320.2.a.bd

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.