Properties

Label 100800.df
Number of curves 4
Conductor 100800
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("100800.df1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800.df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.df1 100800dc4 [0, 0, 0, -1620300, 793798000] [2] 1572864  
100800.df2 100800dc2 [0, 0, 0, -108300, 10582000] [2, 2] 786432  
100800.df3 100800dc1 [0, 0, 0, -36300, -2522000] [2] 393216 \(\Gamma_0(N)\)-optimal
100800.df4 100800dc3 [0, 0, 0, 251700, 66022000] [2] 1572864  

Rank

sage: E.rank()
 

The elliptic curves in class 100800.df have rank \(0\).

Modular form 100800.2.a.df

sage: E.q_eigenform(10)
 
\( q - q^{7} - 6q^{13} + 2q^{17} + 8q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.