Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("4800.bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4800cd

sage: E.isogeny_class().curves
 
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

sage: E.rank()
 

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

Modular form 4800.2.a.bz

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{9} - 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().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

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.