Elliptic curve isogeny class with Cremona label 28224gd (LMFDB label 28224.by)

• Label: 28224gd
• Number of curves: $4$
• Conductor: $28224$
• CM: no
• Rank: $0$

Elliptic curves in class 28224gd

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
28224.by4	28224gd1	[0, 0, 0, 1764, -148176]	[2]	49152	\(\Gamma_0(N)\)-optimal
28224.by3	28224gd2	[0, 0, 0, -33516, -2222640]	[2, 2]	98304
28224.by2	28224gd3	[0, 0, 0, -104076, 10224144]	[2]	196608
28224.by1	28224gd4	[0, 0, 0, -527436, -147435120]	[2]	196608

Rank

The elliptic curves in class 28224gd have rank \(0\).

Complex multiplication

The elliptic curves in class 28224gd do not have complex multiplication.

Modular form 28224.2.a.gd

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.