Elliptic curve isogeny class with Cremona label 222768dx (LMFDB label 222768.z)

• Label: 222768dx
• Number of curves: $4$
• Conductor: $222768$
• CM: no
• Rank: $2$

Elliptic curves in class 222768dx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
222768.z4	222768dx1	\([0, 0, 0, 2454, 141451]\)	\(140119918592/822139227\)	\(-9589431943728\)	\([2]\)	\(393216\)	\(1.1729\)	\(\Gamma_0(N)\)-optimal
222768.z3	222768dx2	\([0, 0, 0, -30351, 1840750]\)	\(16568196345808/1744649361\)	\(325593442347264\)	\([2, 2]\)	\(786432\)	\(1.5195\)
222768.z1	222768dx3	\([0, 0, 0, -472611, 125054386]\)	\(15638954062612612/205211097\)	\(153189263066112\)	\([4]\)	\(1572864\)	\(1.8661\)
222768.z2	222768dx4	\([0, 0, 0, -112971, -12617750]\)	\(213597982529572/31475907099\)	\(23496638745775104\)	\([2]\)	\(1572864\)	\(1.8661\)

Rank

The elliptic curves in class 222768dx have rank \(2\).

Complex multiplication

The elliptic curves in class 222768dx do not have complex multiplication.

Modular form 222768.2.a.dx

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.