Properties

Label 87120.f
Number of curves 4
Conductor 87120
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("87120.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
87120.f1 87120ew4 [0, 0, 0, -7732263, 8275761362] [2] 2488320  
87120.f2 87120ew3 [0, 0, 0, -484968, 128352323] [2] 1244160  
87120.f3 87120ew2 [0, 0, 0, -109263, 7855562] [2] 829440  
87120.f4 87120ew1 [0, 0, 0, -49368, -4135417] [2] 414720 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 87120.f have rank \(0\).

Modular form 87120.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{5} - 4q^{7} + 4q^{13} - 4q^{19} + O(q^{20}) \)

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.