Elliptic curve isogeny class with Cremona label 426888dk (LMFDB label 426888.dk)

• Label: 426888dk
• Number of curves: $2$
• Conductor: $426888$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 426888dk have rank \(0\).

Complex multiplication

The elliptic curves in class 426888dk do not have complex multiplication.

Modular form 426888.2.a.dk

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 426888dk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
426888.dk2	426888dk1	\([0, 0, 0, 4535685, -1060069626]\)	\(66325500/41503\)	\(-6457305390866243730432\)	\([2]\)	\(17694720\)	\(2.8740\)	\(\Gamma_0(N)\)-optimal^*
426888.dk1	426888dk2	\([0, 0, 0, -18943155, -8653126482]\)	\(2415899250/1294139\)	\(402701045284931199916032\)	\([2]\)	\(35389440\)	\(3.2206\)	\(\Gamma_0(N)\)-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 426888dk1.