Elliptic curve isogeny class with LMFDB label 800.d (Cremona label 800a)

• Label: 800.d
• Number of curves: $4$
• Conductor: $800$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 800.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
800.d1	800a2	\([0, 0, 0, -275, -1750]\)	\(287496\)	\(8000000\)	\([2]\)	\(128\)	\(0.18733\)		\(-16\)
800.d2	800a3	\([0, 0, 0, -275, 1750]\)	\(287496\)	\(8000000\)	\([2]\)	\(128\)	\(0.18733\)		\(-16\)
800.d3	800a1	\([0, 0, 0, -25, 0]\)	\(1728\)	\(1000000\)	\([2, 2]\)	\(64\)	\(-0.15924\)	\(\Gamma_0(N)\)-optimal	\(-4\)
800.d4	800a4	\([0, 0, 0, 100, 0]\)	\(1728\)	\(-64000000\)	\([2]\)	\(128\)	\(0.18733\)		\(-4\)

Rank

The elliptic curves in class 800.d have rank \(1\).

Complex multiplication

Each elliptic curve in class 800.d has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 800.2.a.d

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.