Elliptic curve isogeny class with LMFDB label 675.f (Cremona label 675e)

• Label: 675.f
• Number of curves: $2$
• Conductor: $675$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 675.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
675.f1	675e2	\([0, 0, 1, 0, -21094]\)	\(0\)	\(-192216796875\)	\([]\)	\(630\)	\(0.84404\)		\(-3\)
675.f2	675e1	\([0, 0, 1, 0, 781]\)	\(0\)	\(-263671875\)	\([]\)	\(210\)	\(0.29473\)	\(\Gamma_0(N)\)-optimal	\(-3\)

Rank

The elliptic curves in class 675.f have rank \(0\).

Complex multiplication

Each elliptic curve in class 675.f has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 675.2.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.