Elliptic curve isogeny class with LMFDB label 59643.f (Cremona label 59643d)

• Label: 59643.f
• Number of curves: $4$
• Conductor: $59643$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 59643.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
59643.f1	59643d4	\([0, 0, 1, -596430, 177303728]\)	\(-12288000\)	\(-1909505657886363\)	\([]\)	\(317952\)	\(1.9772\)		\(-27\)
59643.f2	59643d2	\([0, 0, 1, -66270, -6566805]\)	\(-12288000\)	\(-2619349324947\)	\([]\)	\(105984\)	\(1.4279\)		\(-27\)
59643.f3	59643d1	\([0, 0, 1, 0, -25956]\)	\(0\)	\(-291038813883\)	\([]\)	\(35328\)	\(0.87861\)	\(\Gamma_0(N)\)-optimal	\(-3\)
59643.f4	59643d3	\([0, 0, 1, 0, 700805]\)	\(0\)	\(-212167295320707\)	\([]\)	\(105984\)	\(1.4279\)		\(-3\)

Rank

The elliptic curves in class 59643.f have rank \(1\).

Complex multiplication

Each elliptic curve in class 59643.f has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 59643.2.a.f

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.