Properties

Label 58800iu
Number of curves $4$
Conductor $58800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("iu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800iu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.jh3 58800iu1 [0, 1, 0, -69008, -4428012] [2] 442368 \(\Gamma_0(N)\)-optimal
58800.jh2 58800iu2 [0, 1, 0, -461008, 117091988] [2, 2] 884736  
58800.jh4 58800iu3 [0, 1, 0, 126992, 395803988] [2] 1769472  
58800.jh1 58800iu4 [0, 1, 0, -7321008, 7621931988] [4] 1769472  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 58800iu do not have complex multiplication.

Modular form 58800.2.a.iu

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{9} + 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.