Properties

Label 81600.ce
Number of curves 6
Conductor 81600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("81600.ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 81600.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
81600.ce1 81600fh6 [0, -1, 0, -44390433, 113851468737] [2] 3145728  
81600.ce2 81600fh4 [0, -1, 0, -2774433, 1779580737] [2, 2] 1572864  
81600.ce3 81600fh5 [0, -1, 0, -2630433, 1972396737] [2] 3145728  
81600.ce4 81600fh2 [0, -1, 0, -182433, 24796737] [2, 2] 786432  
81600.ce5 81600fh1 [0, -1, 0, -54433, -4515263] [2] 393216 \(\Gamma_0(N)\)-optimal
81600.ce6 81600fh3 [0, -1, 0, 361567, 143932737] [2] 1572864  

Rank

sage: E.rank()
 

The elliptic curves in class 81600.ce have rank \(0\).

Modular form 81600.2.a.ce

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{9} - 4q^{11} - 2q^{13} - q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.