Properties

Label 4730.g
Number of curves 4
Conductor 4730
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4730.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4730.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4730.g1 4730g4 [1, -1, 1, -630667, 192931441] [2] 18816  
4730.g2 4730g3 [1, -1, 1, -39847, 2952969] [2] 18816  
4730.g3 4730g2 [1, -1, 1, -39417, 3021941] [2, 2] 9408  
4730.g4 4730g1 [1, -1, 1, -2437, 48749] [4] 4704 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 4730.2.a.g

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

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.