Elliptic curve isogeny class with Cremona label 8550i (LMFDB label 8550.m)

• Label: 8550i
• Number of curves: $3$
• Conductor: $8550$
• CM: no
• Rank: $1$

Elliptic curves in class 8550i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8550.m2	8550i1	$[1, -1, 0, -3492, -78584]$	$-413493625/152$	$-1731375000$	$[]$	$8640$	$0.74058$	$\Gamma_0(N)$-optimal
8550.m3	8550i2	$[1, -1, 0, 2133, -302459]$	$94196375/3511808$	$-40001688000000$	$[]$	$25920$	$1.2899$
8550.m1	8550i3	$[1, -1, 0, -19242, 8268916]$	$-69173457625/2550136832$	$-29047652352000000$	$[]$	$77760$	$1.8392$

Rank

The elliptic curves in class 8550i have rank $1$.

Complex multiplication

The elliptic curves in class 8550i do not have complex multiplication.

Modular form 8550.2.a.i

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.

$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.