Properties

Label 215600.he
Number of curves 4
Conductor 215600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("215600.he1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 215600.he

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
215600.he1 215600er4 [0, -1, 0, -8697908, -9870581188] [2] 5971968  
215600.he2 215600er3 [0, -1, 0, -545533, -152950188] [2] 2985984  
215600.he3 215600er2 [0, -1, 0, -122908, -9331188] [2] 1990656  
215600.he4 215600er1 [0, -1, 0, -55533, 4952312] [2] 995328 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 215600.he have rank \(0\).

Modular form 215600.2.a.he

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

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.