Elliptic curve isogeny class with Cremona label 22080dc (LMFDB label 22080.ck)

• Label: 22080dc
• Number of curves: $4$
• Conductor: $22080$
• CM: no
• Rank: $1$

Elliptic curves in class 22080dc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
22080.ck4	22080dc1	\([0, 1, 0, 29215, -1200225]\)	\(10519294081031/8500170375\)	\(-2228268662784000\)	\([2]\)	\(153600\)	\(1.6328\)	\(\Gamma_0(N)\)-optimal
22080.ck3	22080dc2	\([0, 1, 0, -140065, -10578337]\)	\(1159246431432649/488076890625\)	\(127946428416000000\)	\([2, 2]\)	\(307200\)	\(1.9794\)
22080.ck2	22080dc3	\([0, 1, 0, -1060065, 412437663]\)	\(502552788401502649/10024505152875\)	\(2627863878795264000\)	\([2]\)	\(614400\)	\(2.3260\)
22080.ck1	22080dc4	\([0, 1, 0, -1928545, -1031085025]\)	\(3026030815665395929/1364501953125\)	\(357696000000000000\)	\([2]\)	\(614400\)	\(2.3260\)

Rank

The elliptic curves in class 22080dc have rank \(1\).

Complex multiplication

The elliptic curves in class 22080dc do not have complex multiplication.

Modular form 22080.2.a.dc

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.