Elliptic curve isogeny class with LMFDB label 1728.c (Cremona label 1728e)

• Label: 1728.c
• Number of curves: $3$
• Conductor: $1728$
• CM: no
• Rank: $1$

Elliptic curves in class 1728.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1728.c1	1728e3	\([0, 0, 0, -7884, -357264]\)	\(-1167051/512\)	\(-23776267862016\)	\([]\)	\(3456\)	\(1.2738\)
1728.c2	1728e1	\([0, 0, 0, -204, 1136]\)	\(-132651/2\)	\(-14155776\)	\([]\)	\(384\)	\(0.17521\)	\(\Gamma_0(N)\)-optimal
1728.c3	1728e2	\([0, 0, 0, 756, 5616]\)	\(9261/8\)	\(-41278242816\)	\([]\)	\(1152\)	\(0.72452\)

Rank

The elliptic curves in class 1728.c have rank \(1\).

Complex multiplication

The elliptic curves in class 1728.c do not have complex multiplication.

Modular form 1728.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.