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

• Label: 426888gd
• Number of curves: $2$
• Conductor: $426888$
• CM: no
• Rank: $1$

Elliptic curves in class 426888gd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
426888.gd2	426888gd1	\([0, 0, 0, 2543541, -2762024650]\)	\(8788/21\)	\(-4348797508134409042944\)	\([2]\)	\(16220160\)	\(2.8360\)	\(\Gamma_0(N)\)-optimal^*
426888.gd1	426888gd2	\([0, 0, 0, -20935299, -30603233122]\)	\(2450086/441\)	\(182649495341645179803648\)	\([2]\)	\(32440320\)	\(3.1825\)	\(\Gamma_0(N)\)-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 426888gd1.

Rank

The elliptic curves in class 426888gd have rank \(1\).

Complex multiplication

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

Modular form 426888.2.a.gd

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.