Properties

Label 221760.df
Number of curves $2$
Conductor $221760$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("df1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221760.df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221760.df1 221760lu2 \([0, 0, 0, -18588, -973712]\) \(59466754384/121275\) \(1448500838400\) \([2]\) \(491520\) \(1.2199\)  
221760.df2 221760lu1 \([0, 0, 0, -768, -25688]\) \(-67108864/343035\) \(-256074255360\) \([2]\) \(245760\) \(0.87338\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 221760.df have rank \(1\).

Complex multiplication

The elliptic curves in class 221760.df do not have complex multiplication.

Modular form 221760.2.a.df

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} + q^{11} + 6q^{13} - 2q^{17} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.