Elliptic curve isogeny class with LMFDB label 1089.e (Cremona label 1089b)

• Label: 1089.e
• Number of curves: $2$
• Conductor: $1089$
• CM: $\Q(\sqrt{-3})$
• Rank: $0$

Elliptic curves in class 1089.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
1089.e1	1089b1	$[0, 0, 1, 0, -40263]$	$0$	$-700310464227$	$[]$	$1232$	$0.95178$	$\Gamma_0(N)$-optimal	$-3$
1089.e2	1089b2	$[0, 0, 1, 0, 1087094]$	$0$	$-510526328421483$	$[]$	$3696$	$1.5011$		$-3$

Rank

The elliptic curves in class 1089.e have rank $0$.

Complex multiplication

Each elliptic curve in class 1089.e has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-3})$.

Modular form 1089.2.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.

$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.