Elliptic curve isogeny class with LMFDB label 4400.x (Cremona label 4400j)

• Label: 4400.x
• Number of curves: $2$
• Conductor: $4400$
• CM: no
• Rank: $1$

Elliptic curves in class 4400.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4400.x1	4400j2	$[0, -1, 0, -5708, 104912]$	$41141648/14641$	$7320500000000$	$[2]$	$7680$	$1.1695$
4400.x2	4400j1	$[0, -1, 0, -5083, 141162]$	$464857088/121$	$3781250000$	$[2]$	$3840$	$0.82291$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 4400.x have rank $1$.

Complex multiplication

The elliptic curves in class 4400.x do not have complex multiplication.

Modular form 4400.2.a.x

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.