Elliptic curve isogeny class with LMFDB label 28224.bd (Cremona label 28224ck)

• Label: 28224.bd
• Number of curves: $4$
• Conductor: $28224$
• CM: no
• Rank: $1$

Elliptic curves in class 28224.bd

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
28224.bd1	28224ck4	[0, 0, 0, -527436, 147435120]	[2]	196608
28224.bd2	28224ck3	[0, 0, 0, -104076, -10224144]	[2]	196608
28224.bd3	28224ck2	[0, 0, 0, -33516, 2222640]	[2, 2]	98304
28224.bd4	28224ck1	[0, 0, 0, 1764, 148176]	[2]	49152	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 28224.bd have rank \(1\).

Complex multiplication

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

Modular form 28224.2.a.bd

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.