Elliptic curve isogeny class with Cremona label 450800di (LMFDB label 450800.di)

• Label: 450800di
• Number of curves: $4$
• Conductor: $450800$
• CM: no
• Rank: $1$

Elliptic curves in class 450800di

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
450800.di4	450800di1	\([0, 0, 0, 26950, 3987375]\)	\(73598976/276115\)	\(-8121163408750000\)	\([2]\)	\(1474560\)	\(1.7356\)	\(\Gamma_0(N)\)-optimal^*
450800.di3	450800di2	\([0, 0, 0, -273175, 48105750]\)	\(4790692944/648025\)	\(304957972900000000\)	\([2, 2]\)	\(2949120\)	\(2.0822\)	\(\Gamma_0(N)\)-optimal^*
450800.di1	450800di3	\([0, 0, 0, -4217675, 3333874250]\)	\(4407931365156/100625\)	\(189414890000000000\)	\([2]\)	\(5898240\)	\(2.4287\)	\(\Gamma_0(N)\)-optimal^*
450800.di2	450800di4	\([0, 0, 0, -1130675, -414086750]\)	\(84923690436/9794435\)	\(18436887733040000000\)	\([2]\)	\(5898240\)	\(2.4287\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 450800di1.

Rank

The elliptic curves in class 450800di have rank \(1\).

Complex multiplication

The elliptic curves in class 450800di do not have complex multiplication.

Modular form 450800.2.a.di

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.