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

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

Elliptic curves in class 800a

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality	CM discriminant
800.d3	800a1	[0, 0, 0, -25, 0]	[2, 2]	64	\(\Gamma_0(N)\)-optimal	-4
800.d1	800a2	[0, 0, 0, -275, -1750]	[2]	128		-16
800.d2	800a3	[0, 0, 0, -275, 1750]	[2]	128		-16
800.d4	800a4	[0, 0, 0, 100, 0]	[2]	128		-4

Rank

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

Complex multiplication

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

Modular form 800.2.a.a

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.