Properties

Label 476850.df
Number of curves $2$
Conductor $476850$
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 476850.df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
476850.df1 476850df1 [1, 0, 1, -6531551, 6373664498] [2] 41287680 \(\Gamma_0(N)\)-optimal
476850.df2 476850df2 [1, 0, 1, -1907551, 15224000498] [2] 82575360  

Rank

sage: E.rank()
 

The elliptic curves in class 476850.df have rank \(1\).

Complex multiplication

The elliptic curves in class 476850.df do not have complex multiplication.

Modular form 476850.2.a.df

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - 4q^{7} - q^{8} + q^{9} + q^{11} + q^{12} + 4q^{13} + 4q^{14} + q^{16} - q^{18} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.