Elliptic curve isogeny class with Cremona label 36963e (LMFDB label 36963.h)

• Label: 36963e
• Number of curves: $4$
• Conductor: $36963$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Elliptic curves in class 36963e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
36963.h4	36963e1	\([0, 0, 1, 0, 12663]\)	\(0\)	\(-69274613043\)	\([]\)	\(15876\)	\(0.75900\)	\(\Gamma_0(N)\)-optimal	\(-3\)
36963.h3	36963e2	\([0, 0, 1, 0, -341908]\)	\(0\)	\(-50501192908347\)	\([]\)	\(47628\)	\(1.3083\)		\(-3\)
36963.h2	36963e3	\([0, 0, 1, -41070, 3203802]\)	\(-12288000\)	\(-623471517387\)	\([]\)	\(47628\)	\(1.3083\)		\(-27\)
36963.h1	36963e4	\([0, 0, 1, -369630, -86502661]\)	\(-12288000\)	\(-454510736175123\)	\([]\)	\(142884\)	\(1.8576\)		\(-27\)

Rank

The elliptic curves in class 36963e have rank \(0\).

Complex multiplication

Each elliptic curve in class 36963e has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 36963.2.a.e

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.