Elliptic curve isogeny class with Cremona label 33856ba (LMFDB label 33856.s)

• Label: 33856ba
• Number of curves: $4$
• Conductor: $33856$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 33856ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
33856.s4	33856ba1	\([0, 0, 0, 529, 0]\)	\(1728\)	\(-9474296896\)	\([2]\)	\(12672\)	\(0.60379\)	\(\Gamma_0(N)\)-optimal	\(-4\)
33856.s3	33856ba2	\([0, 0, 0, -2116, 0]\)	\(1728\)	\(606355001344\)	\([2, 2]\)	\(25344\)	\(0.95036\)		\(-4\)
33856.s1	33856ba3	\([0, 0, 0, -23276, -1362704]\)	\(287496\)	\(4850840010752\)	\([2]\)	\(50688\)	\(1.2969\)		\(-16\)
33856.s2	33856ba4	\([0, 0, 0, -23276, 1362704]\)	\(287496\)	\(4850840010752\)	\([2]\)	\(50688\)	\(1.2969\)		\(-16\)

Rank

The elliptic curves in class 33856ba have rank \(1\).

Complex multiplication

Each elliptic curve in class 33856ba has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 33856.2.a.ba

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.