Elliptic curve isogeny class with Cremona label 436800jg (LMFDB label 436800.jg)

• Label: 436800jg
• Number of curves: $3$
• Conductor: $436800$
• CM: no
• Rank: $0$

Elliptic curves in class 436800jg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
436800.jg3	436800jg1	\([0, -1, 0, 21567, -11599263]\)	\(270840023/14329224\)	\(-58692501504000000\)	\([]\)	\(4478976\)	\(1.8973\)	\(\Gamma_0(N)\)-optimal^*
436800.jg2	436800jg2	\([0, -1, 0, -194433, 316072737]\)	\(-198461344537/10417365504\)	\(-42669529104384000000\)	\([]\)	\(13436928\)	\(2.4466\)	\(\Gamma_0(N)\)-optimal^*
436800.jg1	436800jg3	\([0, -1, 0, -41690433, 103625824737]\)	\(-1956469094246217097/36641439744\)	\(-150083337191424000000\)	\([]\)	\(40310784\)	\(2.9959\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 436800jg1.

Rank

The elliptic curves in class 436800jg have rank \(0\).

Complex multiplication

The elliptic curves in class 436800jg do not have complex multiplication.

Modular form 436800.2.a.jg

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.