Elliptic curve isogeny class with Cremona label 4356c (LMFDB label 4356.g)

• Label: 4356c
• Number of curves: $4$
• Conductor: $4356$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 4356c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
4356.g3	4356c1	\([0, 0, 0, 0, -1331]\)	\(0\)	\(-765314352\)	\([2]\)	\(1440\)	\(0.38353\)	\(\Gamma_0(N)\)-optimal	\(-3\)
4356.g2	4356c2	\([0, 0, 0, -1815, -29282]\)	\(54000\)	\(12245029632\)	\([2]\)	\(2880\)	\(0.73011\)		\(-12\)
4356.g4	4356c3	\([0, 0, 0, 0, 35937]\)	\(0\)	\(-557914162608\)	\([2]\)	\(4320\)	\(0.93284\)		\(-3\)
4356.g1	4356c4	\([0, 0, 0, -16335, 790614]\)	\(54000\)	\(8926626601728\)	\([2]\)	\(8640\)	\(1.2794\)		\(-12\)

Rank

The elliptic curves in class 4356c have rank \(1\).

Complex multiplication

Each elliptic curve in class 4356c has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 4356.2.a.c

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.