Elliptic curve isogeny class with LMFDB label 1089.f (Cremona label 1089a)

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

Elliptic curves in class 1089.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
1089.f1	1089a2	\([0, 0, 1, 0, -817]\)	\(0\)	\(-288178803\)	\([]\)	\(336\)	\(0.30214\)		\(-3\)
1089.f2	1089a1	\([0, 0, 1, 0, 30]\)	\(0\)	\(-395307\)	\([3]\)	\(112\)	\(-0.24717\)	\(\Gamma_0(N)\)-optimal	\(-3\)

Rank

The elliptic curves in class 1089.f have rank \(0\).

Complex multiplication

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

Modular form 1089.2.a.f

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.