Elliptic curve isogeny class with Cremona label 428400hq (LMFDB label 428400.hq)

• Label: 428400hq
• Number of curves: $2$
• Conductor: $428400$
• CM: no
• Rank: $1$

Elliptic curves in class 428400hq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
428400.hq2	428400hq1	\([0, 0, 0, 7928925, 61899705250]\)	\(1181569139409959/36161310937500\)	\(-1687142123100000000000000\)	\([2]\)	\(70778880\)	\(3.3288\)	\(\Gamma_0(N)\)-optimal^*
428400.hq1	428400hq2	\([0, 0, 0, -194571075, 996032205250]\)	\(17460273607244690041/918397653311250\)	\(42848760912889680000000000\)	\([2]\)	\(141557760\)	\(3.6754\)	\(\Gamma_0(N)\)-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 428400hq1.

Rank

The elliptic curves in class 428400hq have rank \(1\).

Complex multiplication

The elliptic curves in class 428400hq do not have complex multiplication.

Modular form 428400.2.a.hq

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.