Elliptic curve isogeny class with Cremona label 450528bc (LMFDB label 450528.bc)

• Label: 450528bc
• Number of curves: $4$
• Conductor: $450528$
• CM: no
• Rank: $1$

Elliptic curves in class 450528bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
450528.bc3	450528bc1	\([0, 1, 0, -84594, 9396576]\)	\(22235451328/123201\)	\(370950373445184\)	\([2, 2]\)	\(2322432\)	\(1.6384\)	\(\Gamma_0(N)\)-optimal^*
450528.bc1	450528bc2	\([0, 1, 0, -1351704, 604431432]\)	\(11339065490696/351\)	\(8454709366272\)	\([2]\)	\(4644864\)	\(1.9849\)	\(\Gamma_0(N)\)-optimal^*
450528.bc4	450528bc3	\([0, 1, 0, -37664, 19815036]\)	\(-245314376/6908733\)	\(-166414044456331776\)	\([2]\)	\(4644864\)	\(1.9849\)
450528.bc2	450528bc4	\([0, 1, 0, -133329, -2718945]\)	\(1360251712/771147\)	\(148599971821596672\)	\([2]\)	\(4644864\)	\(1.9849\)

^*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 450528bc1.

Rank

The elliptic curves in class 450528bc have rank \(1\).

Complex multiplication

The elliptic curves in class 450528bc do not have complex multiplication.

Modular form 450528.2.a.bc

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.