Elliptic curve isogeny class with Cremona label 397800dy (LMFDB label 397800.dy)

• Label: 397800dy
• Number of curves: $4$
• Conductor: $397800$
• CM: no
• Rank: $0$

Elliptic curves in class 397800dy

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
397800.dy3	397800dy1	\([0, 0, 0, -100650, -10674875]\)	\(618724784128/87947613\)	\(16028452469250000\)	\([2]\)	\(2621440\)	\(1.8352\)	\(\Gamma_0(N)\)-optimal
397800.dy2	397800dy2	\([0, 0, 0, -425775, 96291250]\)	\(2927363579728/320445801\)	\(934419955716000000\)	\([2, 2]\)	\(5242880\)	\(2.1818\)
397800.dy1	397800dy3	\([0, 0, 0, -6622275, 6559240750]\)	\(2753580869496292/39328497\)	\(458727589008000000\)	\([2]\)	\(10485760\)	\(2.5284\)
397800.dy4	397800dy4	\([0, 0, 0, 568725, 479173750]\)	\(1744147297148/9513325341\)	\(-110963426777424000000\)	\([2]\)	\(10485760\)	\(2.5284\)

Rank

The elliptic curves in class 397800dy have rank \(0\).

Complex multiplication

The elliptic curves in class 397800dy do not have complex multiplication.

Modular form 397800.2.a.dy

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.