Elliptic curve isogeny class with LMFDB label 21168.bv (Cremona label 21168cx)

• Label: 21168.bv
• Number of curves: $4$
• Conductor: $21168$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 21168.bv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
21168.bv1	21168cx4	\([0, 0, 0, -211680, -37488528]\)	\(-12288000\)	\(-85365421682688\)	\([]\)	\(81648\)	\(1.7183\)		\(-27\)
21168.bv2	21168cx3	\([0, 0, 0, -23520, 1388464]\)	\(-12288000\)	\(-117099343872\)	\([]\)	\(27216\)	\(1.1689\)		\(-27\)
21168.bv3	21168cx2	\([0, 0, 0, 0, -148176]\)	\(0\)	\(-9485046853632\)	\([]\)	\(27216\)	\(1.1689\)		\(-3\)
21168.bv4	21168cx1	\([0, 0, 0, 0, 5488]\)	\(0\)	\(-13011038208\)	\([]\)	\(9072\)	\(0.61964\)	\(\Gamma_0(N)\)-optimal	\(-3\)

Rank

The elliptic curves in class 21168.bv have rank \(0\).

Complex multiplication

Each elliptic curve in class 21168.bv has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 21168.2.a.bv

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.