Elliptic curve isogeny class with Cremona label 53361b (LMFDB label 53361.bb)

• Label: 53361b
• Number of curves: $2$
• Conductor: $53361$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 53361b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
53361.bb1	53361b1	\([0, 0, 1, 0, -6603]\)	\(0\)	\(-18833604867\)	\([]\)	\(26208\)	\(0.65046\)	\(\Gamma_0(N)\)-optimal	\(-3\)
53361.bb2	53361b2	\([0, 0, 1, 0, 178274]\)	\(0\)	\(-13729697948043\)	\([]\)	\(78624\)	\(1.1998\)		\(-3\)

Rank

The elliptic curves in class 53361b have rank \(0\).

Complex multiplication

Each elliptic curve in class 53361b has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 53361.2.a.b

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.