Elliptic curve isogeny class with LMFDB label 550.e (Cremona label 550f)

• Label: 550.e
• Number of curves: $3$
• Conductor: $550$
• CM: no
• Rank: $1$

Elliptic curves in class 550.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
550.e1	550f3	$[1, 0, 1, -758201, 254051548]$	$-24680042791780949/369098752$	$-720896000000000$	$[]$	$6000$	$1.9878$
550.e2	550f1	$[1, 0, 1, -701, -7202]$	$-19465109/22$	$-42968750$	$[]$	$240$	$0.37841$	$\Gamma_0(N)$-optimal
550.e3	550f2	$[1, 0, 1, 4924, 75298]$	$6761990971/5153632$	$-10065687500000$	$[]$	$1200$	$1.1831$

Rank

The elliptic curves in class 550.e have rank $1$.

Complex multiplication

The elliptic curves in class 550.e do not have complex multiplication.

Modular form 550.2.a.e

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.

$\left(\begin{array}{rrr} 1 & 25 & 5 \\ 25 & 1 & 5 \\ 5 & 5 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.