Properties

Label 58800.be
Number of curves $2$
Conductor $58800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("58800.be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.be1 58800fp1 [0, -1, 0, -6008, 70512] [2] 110592 \(\Gamma_0(N)\)-optimal
58800.be2 58800fp2 [0, -1, 0, 21992, 518512] [2] 221184  

Rank

sage: E.rank()
 

The elliptic curves in class 58800.be have rank \(1\).

Modular form 58800.2.a.be

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

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.