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

• Label: 453024.dc
• Number of curves: $4$
• Conductor: $453024$
• CM: no
• Rank: $1$

Elliptic curves in class 453024.dc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
453024.dc1	453024dc2	\([0, 0, 0, -4077579, 3169214818]\)	\(11339065490696/351\)	\(232092291644928\)	\([2]\)	\(7864320\)	\(2.2610\)	\(\Gamma_0(N)\)-optimal^*
453024.dc2	453024dc4	\([0, 0, 0, -402204, -14012768]\)	\(1360251712/771147\)	\(4079254117951254528\)	\([2]\)	\(7864320\)	\(2.2610\)
453024.dc3	453024dc1	\([0, 0, 0, -255189, 49380100]\)	\(22235451328/123201\)	\(10183049295921216\)	\([2, 2]\)	\(3932160\)	\(1.9144\)	\(\Gamma_0(N)\)-optimal^*
453024.dc4	453024dc3	\([0, 0, 0, -113619, 103884550]\)	\(-245314376/6908733\)	\(-4568272576447117824\)	\([2]\)	\(7864320\)	\(2.2610\)

^*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 453024.dc1.

Rank

The elliptic curves in class 453024.dc have rank \(1\).

Complex multiplication

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

Modular form 453024.2.a.dc

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.