Elliptic curve isogeny class with Cremona label 82800cm (LMFDB label 82800.m)

• Label: 82800cm
• Number of curves: $4$
• Conductor: $82800$
• CM: no
• Rank: $0$

Elliptic curves in class 82800cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
82800.m4	82800cm1	\([0, 0, 0, -276675, -11090750]\)	\(1355469437763/753664000\)	\(1302331392000000000\)	\([2]\)	\(995328\)	\(2.1663\)	\(\Gamma_0(N)\)-optimal
82800.m3	82800cm2	\([0, 0, 0, -3348675, -2355026750]\)	\(2403250125069123/4232000000\)	\(7312896000000000000\)	\([2]\)	\(1990656\)	\(2.5128\)
82800.m2	82800cm3	\([0, 0, 0, -13716675, 19553069250]\)	\(226568219476347/3893440\)	\(4904613089280000000\)	\([2]\)	\(2985984\)	\(2.7156\)
82800.m1	82800cm4	\([0, 0, 0, -14148675, 18255773250]\)	\(248656466619387/29607177800\)	\(37296517160793600000000\)	\([2]\)	\(5971968\)	\(3.0621\)

Rank

The elliptic curves in class 82800cm have rank \(0\).

Complex multiplication

The elliptic curves in class 82800cm do not have complex multiplication.

Modular form 82800.2.a.cm

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.