Elliptic curve isogeny class with Cremona label 108900bc (LMFDB label 108900.c)

• Label: 108900bc
• Number of curves: $2$
• Conductor: $108900$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $2$

Elliptic curves in class 108900bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
108900.c2	108900bc1	\([0, 0, 0, 0, 3025]\)	\(0\)	\(-3953070000\)	\([3]\)	\(67392\)	\(0.52036\)	\(\Gamma_0(N)\)-optimal	\(-3\)
108900.c1	108900bc2	\([0, 0, 0, 0, -81675]\)	\(0\)	\(-2881788030000\)	\([]\)	\(202176\)	\(1.0697\)		\(-3\)

Rank

The elliptic curves in class 108900bc have rank \(2\).

Complex multiplication

Each elliptic curve in class 108900bc has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 108900.2.a.bc

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.