Elliptic curve isogeny class with LMFDB label 73008.bs (Cremona label 73008bi)

• Label: 73008.bs
• Number of curves: $4$
• Conductor: $73008$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 73008.bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
73008.bs1	73008bi4	\([0, 0, 0, -730080, 240123312]\)	\(-12288000\)	\(-3502304190148608\)	\([]\)	\(443232\)	\(2.0278\)		\(-27\)
73008.bs2	73008bi2	\([0, 0, 0, -81120, -8893456]\)	\(-12288000\)	\(-4804258148352\)	\([]\)	\(147744\)	\(1.4785\)		\(-27\)
73008.bs3	73008bi1	\([0, 0, 0, 0, -35152]\)	\(0\)	\(-533806460928\)	\([]\)	\(49248\)	\(0.92916\)	\(\Gamma_0(N)\)-optimal	\(-3\)
73008.bs4	73008bi3	\([0, 0, 0, 0, 949104]\)	\(0\)	\(-389144910016512\)	\([]\)	\(147744\)	\(1.4785\)		\(-3\)

Rank

The elliptic curves in class 73008.bs have rank \(0\).

Complex multiplication

Each elliptic curve in class 73008.bs has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 73008.2.a.bs

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.