Elliptic curve isogeny class with LMFDB label 1728.y (Cremona label 1728j)

• Label: 1728.y
• Number of curves: $3$
• Conductor: $1728$
• CM: no
• Rank: $0$

Elliptic curves in class 1728.y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1728.y1	1728j2	$[0, 0, 0, -1836, -30672]$	$-132651/2$	$-10319560704$	$[]$	$1152$	$0.72452$
1728.y2	1728j3	$[0, 0, 0, -876, 13232]$	$-1167051/512$	$-32614907904$	$[]$	$1152$	$0.72452$
1728.y3	1728j1	$[0, 0, 0, 84, -208]$	$9261/8$	$-56623104$	$[]$	$384$	$0.17521$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1728.y have rank $0$.

Complex multiplication

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

Modular form 1728.2.a.y

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.