Elliptic curve isogeny class with LMFDB label 1008.b (Cremona label 1008e)

• Label: 1008.b
• Number of curves: $4$
• Conductor: $1008$
• CM: no
• Rank: $0$

Elliptic curves in class 1008.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1008.b1	1008e4	$[0, 0, 0, -36291, 2661010]$	$7080974546692/189$	$141087744$	$[4]$	$1536$	$1.0775$
1008.b2	1008e3	$[0, 0, 0, -3531, -9686]$	$6522128932/3720087$	$2777030065152$	$[2]$	$1536$	$1.0775$
1008.b3	1008e2	$[0, 0, 0, -2271, 41470]$	$6940769488/35721$	$6666395904$	$[2, 2]$	$768$	$0.73092$
1008.b4	1008e1	$[0, 0, 0, -66, 1339]$	$-2725888/64827$	$-756142128$	$[2]$	$384$	$0.38435$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1008.b have rank $0$.

Complex multiplication

The elliptic curves in class 1008.b do not have complex multiplication.

Modular form 1008.2.a.b

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.