Elliptic curve isogeny class with LMFDB label 458640.db (Cremona label 458640db)

• Label: 458640.db
• Number of curves: $4$
• Conductor: $458640$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 458640.db have rank \(0\).

Complex multiplication

The elliptic curves in class 458640.db do not have complex multiplication.

Modular form 458640.2.a.db

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 458640.db

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
458640.db1	458640db4	\([0, 0, 0, -8439123, 8955954322]\)	\(189208196468929/10860320250\)	\(3815209126544385024000\)	\([2]\)	\(19906560\)	\(2.8952\)	\(\Gamma_0(N)\)-optimal^*
458640.db2	458640db2	\([0, 0, 0, -1453683, -671633102]\)	\(967068262369/4928040\)	\(1731210751724912640\)	\([2]\)	\(6635520\)	\(2.3459\)	\(\Gamma_0(N)\)-optimal^*
458640.db3	458640db1	\([0, 0, 0, -42483, -21634382]\)	\(-24137569/561600\)	\(-197288974555545600\)	\([2]\)	\(3317760\)	\(1.9994\)	\(\Gamma_0(N)\)-optimal^*
458640.db4	458640db3	\([0, 0, 0, 380877, 571662322]\)	\(17394111071/411937500\)	\(-144712832898816000000\)	\([2]\)	\(9953280\)	\(2.5487\)	\(\Gamma_0(N)\)-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 458640.db1.