Elliptic curve isogeny class with Cremona label 405600cc (LMFDB label 405600.cc)

• Label: 405600cc
• Number of curves: $4$
• Conductor: $405600$
• CM: no
• Rank: $1$

Elliptic curves in class 405600cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
405600.cc3	405600cc1	\([0, -1, 0, -990058, 377685112]\)	\(22235451328/123201\)	\(594667695609000000\)	\([2, 2]\)	\(8257536\)	\(2.2533\)	\(\Gamma_0(N)\)-optimal^*
405600.cc1	405600cc2	\([0, -1, 0, -15819808, 24223923112]\)	\(11339065490696/351\)	\(13553679672000000\)	\([2]\)	\(16515072\)	\(2.5999\)	\(\Gamma_0(N)\)-optimal^*
405600.cc4	405600cc3	\([0, -1, 0, -440808, 794016612]\)	\(-245314376/6908733\)	\(-266777076983976000000\)	\([2]\)	\(16515072\)	\(2.5999\)
405600.cc2	405600cc4	\([0, -1, 0, -1560433, -106563263]\)	\(1360251712/771147\)	\(238219473915072000000\)	\([2]\)	\(16515072\)	\(2.5999\)

^*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 405600cc1.

Rank

The elliptic curves in class 405600cc have rank \(1\).

Complex multiplication

The elliptic curves in class 405600cc do not have complex multiplication.

Modular form 405600.2.a.cc

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.