Elliptic Curve Isogeny Class with Cremona label 4800cd (LMFDB label 4800.bz)

• Label: 4800cd
• Number of curves: 8
• Conductor: 4800
• CM: no
• Rank: 1

Elliptic curves in class 4800cd

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
4800.bz7	4800cd1	[0, 1, 0, -33, -11937]	[2]	3072	\(\Gamma_0(N)\)-optimal
4800.bz6	4800cd2	[0, 1, 0, -8033, -275937]	[2, 2]	6144
4800.bz4	4800cd3	[0, 1, 0, -128033, -17675937]	[2]	12288
4800.bz5	4800cd4	[0, 1, 0, -16033, 356063]	[2, 2]	12288
4800.bz2	4800cd5	[0, 1, 0, -216033, 38556063]	[2, 2]	24576
4800.bz8	4800cd6	[0, 1, 0, 55967, 2732063]	[2]	24576
4800.bz1	4800cd7	[0, 1, 0, -3456033, 2471796063]	[2]	49152
4800.bz3	4800cd8	[0, 1, 0, -176033, 53316063]	[2]	49152

Rank

The elliptic curves in class 4800cd have rank \(1\).

Modular form 4800.2.a.bz

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 2 & 2 \\ 8 & 4 & 8 & 2 & 4 & 1 & 8 & 8 \\ 16 & 8 & 16 & 4 & 2 & 8 & 1 & 4 \\ 16 & 8 & 16 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.