Properties

Label 58800iz
Number of curves $6$
Conductor $58800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("58800.fr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800iz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.fr6 58800iz1 [0, 1, 0, 195592, -46528812] [2] 884736 \(\Gamma_0(N)\)-optimal
58800.fr5 58800iz2 [0, 1, 0, -1372408, -482432812] [2, 2] 1769472  
58800.fr4 58800iz3 [0, 1, 0, -7252408, 7102767188] [2] 3538944  
58800.fr2 58800iz4 [0, 1, 0, -20580408, -35940400812] [2, 2] 3538944  
58800.fr3 58800iz5 [0, 1, 0, -19208408, -40937224812] [2] 7077888  
58800.fr1 58800iz6 [0, 1, 0, -329280408, -2299946200812] [2] 7077888  

Rank

sage: E.rank()
 

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

Modular form 58800.2.a.fr

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

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.