Elliptic curve isogeny class with LMFDB label 7803.k (Cremona label 7803a)

• Label: 7803.k
• Number of curves: $4$
• Conductor: $7803$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 7803.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
7803.k1	7803a4	\([0, 0, 1, -78030, -8390176]\)	\(-12288000\)	\(-4275897935643\)	\([]\)	\(15552\)	\(1.4688\)		\(-27\)
7803.k2	7803a3	\([0, 0, 1, -8670, 310747]\)	\(-12288000\)	\(-5865429267\)	\([]\)	\(5184\)	\(0.91945\)		\(-27\)
7803.k3	7803a2	\([0, 0, 1, 0, -33163]\)	\(0\)	\(-475099770627\)	\([]\)	\(5184\)	\(0.91945\)		\(-3\)
7803.k4	7803a1	\([0, 0, 1, 0, 1228]\)	\(0\)	\(-651714363\)	\([]\)	\(1728\)	\(0.37014\)	\(\Gamma_0(N)\)-optimal	\(-3\)

Rank

The elliptic curves in class 7803.k have rank \(1\).

Complex multiplication

Each elliptic curve in class 7803.k has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 7803.2.a.k

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.