Elliptic curve isogeny class with Cremona label 438080ck (LMFDB label 438080.ck)

• Label: 438080ck
• Number of curves: $2$
• Conductor: $438080$
• CM: no
• Rank: $0$

Elliptic curves in class 438080ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
438080.ck2	438080ck1	\([0, 1, 0, -992981, 147410675]\)	\(2575826944/1266325\)	\(53232328620063539200\)	\([]\)	\(6303744\)	\(2.4783\)	\(\Gamma_0(N)\)-optimal^*
438080.ck1	438080ck2	\([0, 1, 0, -65828821, 205553835379]\)	\(750484394082304/578125\)	\(24302560546048000000\)	\([]\)	\(18911232\)	\(3.0276\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 438080ck1.

Rank

The elliptic curves in class 438080ck have rank \(0\).

Complex multiplication

The elliptic curves in class 438080ck do not have complex multiplication.

Modular form 438080.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.