Elliptic curve isogeny class with Cremona label 1002d (LMFDB label 1002.d)

• Label: 1002d
• Number of curves: $2$
• Conductor: $1002$
• CM: no
• Rank: $1$

Elliptic curves in class 1002d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1002.d2	1002d1	$[1, 0, 1, -5, -16]$	$-10218313/96192$	$-96192$	$[2]$	$144$	$-0.36143$	$\Gamma_0(N)$-optimal
1002.d1	1002d2	$[1, 0, 1, -125, -544]$	$213525509833/669336$	$669336$	$[2]$	$288$	$-0.014852$

Rank

The elliptic curves in class 1002d have rank $1$.

Complex multiplication

The elliptic curves in class 1002d do not have complex multiplication.

Modular form 1002.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.