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

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

Elliptic curves in class 450800.ga

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
450800.ga1	450800ga3	\([0, -1, 0, -33144008, -72798473488]\)	\(534774372149809/5323062500\)	\(40080190724000000000000\)	\([2]\)	\(47775744\)	\(3.1557\)
450800.ga2	450800ga4	\([0, -1, 0, -8644008, -178050473488]\)	\(-9486391169809/1813439640250\)	\(-13654359055089424000000000\)	\([2]\)	\(95551488\)	\(3.5023\)
450800.ga3	450800ga1	\([0, -1, 0, -2960008, 1904182512]\)	\(380920459249/12622400\)	\(95040815206400000000\)	\([2]\)	\(15925248\)	\(2.6064\)	\(\Gamma_0(N)\)-optimal^*
450800.ga4	450800ga2	\([0, -1, 0, 959992, 6576822512]\)	\(12994449551/2489452840\)	\(-18744424779082240000000\)	\([2]\)	\(31850496\)	\(2.9530\)

^*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 450800.ga1.

Rank

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

Complex multiplication

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

Modular form 450800.2.a.ga

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.