Elliptic curve isogeny class with Cremona label 16928e (LMFDB label 16928.d)

• Label: 16928e
• Number of curves: $4$
• Conductor: $16928$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 16928e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
16928.d3	16928e1	\([0, 0, 0, -529, 0]\)	\(1728\)	\(9474296896\)	\([2, 2]\)	\(6336\)	\(0.60379\)	\(\Gamma_0(N)\)-optimal	\(-4\)
16928.d1	16928e2	\([0, 0, 0, -5819, -170338]\)	\(287496\)	\(75794375168\)	\([2]\)	\(12672\)	\(0.95036\)		\(-16\)
16928.d2	16928e3	\([0, 0, 0, -5819, 170338]\)	\(287496\)	\(75794375168\)	\([2]\)	\(12672\)	\(0.95036\)		\(-16\)
16928.d4	16928e4	\([0, 0, 0, 2116, 0]\)	\(1728\)	\(-606355001344\)	\([2]\)	\(12672\)	\(0.95036\)		\(-4\)

Rank

The elliptic curves in class 16928e have rank \(1\).

Complex multiplication

Each elliptic curve in class 16928e has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 16928.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.