Properties

Label 4800.cq
Number of curves 8
Conductor 4800
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("4800.cq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4800.cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4800.cq1 4800w7 [0, 1, 0, -8533633, -9597935137] [2] 110592  
4800.cq2 4800w8 [0, 1, 0, -725633, -32623137] [2] 110592  
4800.cq3 4800w6 [0, 1, 0, -533633, -149935137] [2, 2] 55296  
4800.cq4 4800w5 [0, 1, 0, -461633, 120568863] [2] 36864  
4800.cq5 4800w4 [0, 1, 0, -109633, -12071137] [2] 36864  
4800.cq6 4800w2 [0, 1, 0, -29633, 1768863] [2, 2] 18432  
4800.cq7 4800w3 [0, 1, 0, -21633, -4015137] [2] 27648  
4800.cq8 4800w1 [0, 1, 0, 2367, 136863] [2] 9216 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 4800.2.a.cq

sage: E.q_eigenform(10)
 
\( q + q^{3} + 4q^{7} + q^{9} + 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.