Elliptic curve isogeny class with Cremona label 43200fk (LMFDB label 43200.eg)

• Label: 43200fk
• Number of curves: $4$
• Conductor: $43200$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 43200fk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
43200.eg3	43200fk1	\([0, 0, 0, 0, -250]\)	\(0\)	\(-27000000\)	\([]\)	\(6912\)	\(0.10483\)	\(\Gamma_0(N)\)-optimal	\(-3\)
43200.eg2	43200fk2	\([0, 0, 0, -3000, -63250]\)	\(-12288000\)	\(-243000000\)	\([]\)	\(20736\)	\(0.65413\)		\(-27\)
43200.eg4	43200fk3	\([0, 0, 0, 0, 6750]\)	\(0\)	\(-19683000000\)	\([]\)	\(20736\)	\(0.65413\)		\(-3\)
43200.eg1	43200fk4	\([0, 0, 0, -27000, 1707750]\)	\(-12288000\)	\(-177147000000\)	\([]\)	\(62208\)	\(1.2034\)		\(-27\)

Rank

The elliptic curves in class 43200fk have rank \(0\).

Complex multiplication

Each elliptic curve in class 43200fk has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 43200.2.a.fk

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.