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

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

Elliptic curves in class 428400mo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
428400.mo2	428400mo1	\([0, 0, 0, 293325, 73003250]\)	\(59822347031/83966400\)	\(-3917536358400000000\)	\([2]\)	\(5308416\)	\(2.2533\)	\(\Gamma_0(N)\)-optimal^*
428400.mo1	428400mo2	\([0, 0, 0, -1866675, 723163250]\)	\(15417797707369/4080067320\)	\(190359620881920000000\)	\([2]\)	\(10616832\)	\(2.5999\)	\(\Gamma_0(N)\)-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 428400mo1.

Rank

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

Complex multiplication

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

Modular form 428400.2.a.mo

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.