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

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

Elliptic curves in class 450528.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
450528.f1	450528f4	\([0, -1, 0, -1351704, -604431432]\)	\(11339065490696/351\)	\(8454709366272\)	\([2]\)	\(4644864\)	\(1.9849\)
450528.f2	450528f2	\([0, -1, 0, -133329, 2718945]\)	\(1360251712/771147\)	\(148599971821596672\)	\([2]\)	\(4644864\)	\(1.9849\)	\(\Gamma_0(N)\)-optimal^*
450528.f3	450528f1	\([0, -1, 0, -84594, -9396576]\)	\(22235451328/123201\)	\(370950373445184\)	\([2, 2]\)	\(2322432\)	\(1.6384\)	\(\Gamma_0(N)\)-optimal^*
450528.f4	450528f3	\([0, -1, 0, -37664, -19815036]\)	\(-245314376/6908733\)	\(-166414044456331776\)	\([2]\)	\(4644864\)	\(1.9849\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 450528.f1.

Rank

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

Complex multiplication

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

Modular form 450528.2.a.f

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.