Properties

Label 4800.cj
Number of curves 4
Conductor 4800
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4800.cj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4800.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4800.cj1 4800cl4 [0, 1, 0, -52993, -4697857] [2] 15360  
4800.cj2 4800cl2 [0, 1, 0, -3393, 74943] [2] 3072  
4800.cj3 4800cl3 [0, 1, 0, -1793, -141057] [2] 7680  
4800.cj4 4800cl1 [0, 1, 0, -193, 1343] [2] 1536 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4800.cj have rank \(0\).

Modular form 4800.2.a.cj

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{7} + q^{9} + 2q^{11} + 6q^{13} - 2q^{17} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.