Elliptic curve isogeny class with Cremona label 54080ck (LMFDB label 54080.m)

• Label: 54080ck
• Number of curves: $4$
• Conductor: $54080$
• CM: no
• Rank: $2$

Elliptic curves in class 54080ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54080.m3	54080ck1	\([0, 1, 0, -901, -7461]\)	\(16384/5\)	\(24713262080\)	\([2]\)	\(36864\)	\(0.69910\)	\(\Gamma_0(N)\)-optimal
54080.m4	54080ck2	\([0, 1, 0, 2479, -47345]\)	\(21296/25\)	\(-1977060966400\)	\([2]\)	\(73728\)	\(1.0457\)
54080.m1	54080ck3	\([0, 1, 0, -27941, 1787995]\)	\(488095744/125\)	\(617831552000\)	\([2]\)	\(110592\)	\(1.2484\)
54080.m2	54080ck4	\([0, 1, 0, -24561, 2240239]\)	\(-20720464/15625\)	\(-1235663104000000\)	\([2]\)	\(221184\)	\(1.5950\)

Rank

The elliptic curves in class 54080ck have rank \(2\).

Complex multiplication

The elliptic curves in class 54080ck do not have complex multiplication.

Modular form 54080.2.a.ck

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.