Properties

Label 72600n
Number of curves 4
Conductor 72600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("72600.ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72600n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
72600.ce4 72600n1 [0, -1, 0, 2017, -955788] [2] 368640 \(\Gamma_0(N)\)-optimal
72600.ce3 72600n2 [0, -1, 0, -134108, -18379788] [2, 2] 737280  
72600.ce2 72600n3 [0, -1, 0, -315608, 42241212] [2] 1474560  
72600.ce1 72600n4 [0, -1, 0, -2130608, -1196314788] [2] 1474560  

Rank

sage: E.rank()
 

The elliptic curves in class 72600n have rank \(0\).

Modular form 72600.2.a.ce

sage: E.q_eigenform(10)
 
\( q - q^{3} + 4q^{7} + q^{9} + 6q^{13} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.