Elliptic curve isogeny class with Cremona label 52272bj (LMFDB label 52272.bk)

• Label: 52272bj
• Number of curves: $4$
• Conductor: $52272$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 52272bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
52272.bk4	52272bj1	\([0, 0, 0, 0, 21296]\)	\(0\)	\(-195920474112\)	\([]\)	\(34560\)	\(0.84563\)	\(\Gamma_0(N)\)-optimal	\(-3\)
52272.bk2	52272bj2	\([0, 0, 0, -58080, 5387888]\)	\(-12288000\)	\(-1763284267008\)	\([]\)	\(103680\)	\(1.3949\)		\(-27\)
52272.bk3	52272bj3	\([0, 0, 0, 0, -574992]\)	\(0\)	\(-142826025627648\)	\([]\)	\(103680\)	\(1.3949\)		\(-3\)
52272.bk1	52272bj4	\([0, 0, 0, -522720, -145472976]\)	\(-12288000\)	\(-1285434230648832\)	\([]\)	\(311040\)	\(1.9442\)		\(-27\)

Rank

The elliptic curves in class 52272bj have rank \(1\).

Complex multiplication

Each elliptic curve in class 52272bj has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 52272.2.a.bj

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 3 & 9 \\ 3 & 1 & 9 & 27 \\ 3 & 9 & 1 & 3 \\ 9 & 27 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.