Elliptic curve isogeny class with LMFDB label 2550.d (Cremona label 2550a)

• Label: 2550.d
• Number of curves: $4$
• Conductor: $2550$
• CM: no
• Rank: $1$

Elliptic curves in class 2550.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2550.d1	2550a3	$[1, 1, 0, -4650, -123750]$	$711882749089/1721250$	$26894531250$	$[2]$	$3072$	$0.88009$
2550.d2	2550a4	$[1, 1, 0, -4150, 100750]$	$506071034209/2505630$	$39150468750$	$[2]$	$3072$	$0.88009$
2550.d3	2550a2	$[1, 1, 0, -400, -500]$	$454756609/260100$	$4064062500$	$[2, 2]$	$1536$	$0.53352$
2550.d4	2550a1	$[1, 1, 0, 100, 0]$	$6967871/4080$	$-63750000$	$[2]$	$768$	$0.18695$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 2550.d have rank $1$.

Complex multiplication

The elliptic curves in class 2550.d do not have complex multiplication.

Modular form 2550.2.a.d

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.