Elliptic curve isogeny class with LMFDB label 8800.n (Cremona label 8800a)

• Label: 8800.n
• Number of curves: $4$
• Conductor: $8800$
• CM: no
• Rank: $1$

Elliptic curves in class 8800.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8800.n1	8800a2	$[0, 0, 0, -14675, -684250]$	$43688592648/55$	$440000000$	$[2]$	$6144$	$0.93729$
8800.n2	8800a3	$[0, 0, 0, -2300, 28000]$	$21024576/6875$	$440000000000$	$[2]$	$6144$	$0.93729$
8800.n3	8800a1	$[0, 0, 0, -925, -10500]$	$87528384/3025$	$3025000000$	$[2, 2]$	$3072$	$0.59072$	$\Gamma_0(N)$-optimal
8800.n4	8800a4	$[0, 0, 0, 325, -36750]$	$474552/73205$	$-585640000000$	$[2]$	$6144$	$0.93729$

Rank

The elliptic curves in class 8800.n have rank $1$.

Complex multiplication

The elliptic curves in class 8800.n do not have complex multiplication.

Modular form 8800.2.a.n

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.