Properties

Label 4730.a
Number of curves 2
Conductor 4730
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4730.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4730.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4730.a1 4730c2 [1, 0, 1, -117418, 15476508] [2] 13536  
4730.a2 4730c1 [1, 0, 1, -7338, 241436] [2] 6768 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4730.a have rank \(0\).

Modular form 4730.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} - 2q^{3} + q^{4} + q^{5} + 2q^{6} - q^{8} + q^{9} - q^{10} + q^{11} - 2q^{12} + 2q^{13} - 2q^{15} + q^{16} + 6q^{17} - q^{18} + 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.