Properties

Label 4730.h
Number of curves 2
Conductor 4730
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4730.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4730.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4730.h1 4730e1 [1, 0, 0, -3916, 96400] [3] 5760 \(\Gamma_0(N)\)-optimal
4730.h2 4730e2 [1, 0, 0, 17844, 373136] [] 17280  

Rank

sage: E.rank()
 

The elliptic curves in class 4730.h have rank \(1\).

Modular form 4730.2.a.h

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + q^{8} - 2q^{9} - q^{10} - q^{11} + q^{12} - 4q^{13} + 2q^{14} - q^{15} + q^{16} - 2q^{18} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.