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

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

Elliptic curves in class 426888.gj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
426888.gj1	426888gj2	\([0, 0, 0, -658119, 205439850]\)	\(21882096/7\)	\(10084308438226176\)	\([2]\)	\(4300800\)	\(2.0456\)	\(\Gamma_0(N)\)-optimal^*
426888.gj2	426888gj1	\([0, 0, 0, -35574, 4108797]\)	\(-55296/49\)	\(-4411884941723952\)	\([2]\)	\(2150400\)	\(1.6990\)	\(\Gamma_0(N)\)-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 426888.gj1.

Rank

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

Complex multiplication

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

Modular form 426888.2.a.gj

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.