Properties

Label 58800.gt
Number of curves $2$
Conductor $58800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("58800.gt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800.gt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.gt1 58800il1 [0, 1, 0, -294408, -23596812] [2] 774144 \(\Gamma_0(N)\)-optimal
58800.gt2 58800il2 [0, 1, 0, 1077592, -180004812] [2] 1548288  

Rank

sage: E.rank()
 

The elliptic curves in class 58800.gt have rank \(0\).

Modular form 58800.2.a.gt

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.