Elliptic curve isogeny class with Cremona label 453024dd (LMFDB label 453024.dd)

• Label: 453024dd
• Number of curves: $4$
• Conductor: $453024$
• CM: no
• Rank: $0$

Elliptic curves in class 453024dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
453024.dd3	453024dd1	\([0, 0, 0, -255189, -49380100]\)	\(22235451328/123201\)	\(10183049295921216\)	\([2, 2]\)	\(3932160\)	\(1.9144\)	\(\Gamma_0(N)\)-optimal^*
453024.dd2	453024dd2	\([0, 0, 0, -402204, 14012768]\)	\(1360251712/771147\)	\(4079254117951254528\)	\([2]\)	\(7864320\)	\(2.2610\)	\(\Gamma_0(N)\)-optimal^*
453024.dd4	453024dd3	\([0, 0, 0, -113619, -103884550]\)	\(-245314376/6908733\)	\(-4568272576447117824\)	\([2]\)	\(7864320\)	\(2.2610\)
453024.dd1	453024dd4	\([0, 0, 0, -4077579, -3169214818]\)	\(11339065490696/351\)	\(232092291644928\)	\([2]\)	\(7864320\)	\(2.2610\)

^*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 453024dd1.

Rank

The elliptic curves in class 453024dd have rank \(0\).

Complex multiplication

The elliptic curves in class 453024dd do not have complex multiplication.

Modular form 453024.2.a.dd

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.