Elliptic curve isogeny class with LMFDB label 108900.j (Cremona label 108900n)

• Label: 108900.j
• Number of curves: $4$
• Conductor: $108900$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 108900.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
108900.j1	108900n4	\([0, 0, 0, -408375, 98826750]\)	\(54000\)	\(139478540652000000\)	\([2]\)	\(1244160\)	\(2.0841\)		\(-12\)
108900.j2	108900n2	\([0, 0, 0, -45375, -3660250]\)	\(54000\)	\(191328588000000\)	\([2]\)	\(414720\)	\(1.5348\)		\(-12\)
108900.j3	108900n1	\([0, 0, 0, 0, -166375]\)	\(0\)	\(-11958036750000\)	\([2]\)	\(207360\)	\(1.1883\)	\(\Gamma_0(N)\)-optimal	\(-3\)
108900.j4	108900n3	\([0, 0, 0, 0, 4492125]\)	\(0\)	\(-8717408790750000\)	\([2]\)	\(622080\)	\(1.7376\)		\(-3\)

Rank

The elliptic curves in class 108900.j have rank \(1\).

Complex multiplication

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

Modular form 108900.2.a.j

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.