Properties

Label 118580.ba
Number of curves 4
Conductor 118580
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("118580.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 118580.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
118580.ba1 118580m4 [0, -1, 0, -42097876, -105118787640] [2] 7464960  
118580.ba2 118580m3 [0, -1, 0, -2640381, -1629669754] [2] 3732480  
118580.ba3 118580m2 [0, -1, 0, -594876, -99596440] [2] 2488320  
118580.ba4 118580m1 [0, -1, 0, -268781, 52624706] [2] 1244160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 118580.ba have rank \(0\).

Modular form 118580.2.a.ba

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} + q^{9} - 4q^{13} - 2q^{15} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.