Properties

Label 4800.bq
Number of curves 2
Conductor 4800
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4800.bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4800.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4800.bq1 4800bf1 [0, 1, 0, -33, -87] [] 480 \(\Gamma_0(N)\)-optimal
4800.bq2 4800bf2 [0, 1, 0, 167, 3713] [] 2400  

Rank

sage: E.rank()
 

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

Modular form 4800.2.a.bq

sage: E.q_eigenform(10)
 
\( q + q^{3} - 3q^{7} + q^{9} - 2q^{11} - q^{13} + 2q^{17} + 5q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.