Elliptic Curve Isogeny Class with Cremona label 4800b (LMFDB label 4800.t)

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

Elliptic curves in class 4800b

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
4800.t7	4800b1	[0, -1, 0, -33, 11937]	[2]	3072	\(\Gamma_0(N)\)-optimal
4800.t6	4800b2	[0, -1, 0, -8033, 275937]	[2, 2]	6144
4800.t5	4800b3	[0, -1, 0, -16033, -356063]	[2, 2]	12288
4800.t4	4800b4	[0, -1, 0, -128033, 17675937]	[2]	12288
4800.t2	4800b5	[0, -1, 0, -216033, -38556063]	[2, 2]	24576
4800.t8	4800b6	[0, -1, 0, 55967, -2732063]	[2]	24576
4800.t1	4800b7	[0, -1, 0, -3456033, -2471796063]	[2]	49152
4800.t3	4800b8	[0, -1, 0, -176033, -53316063]	[2]	49152

Rank

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

Modular form 4800.2.a.t

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.