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Properties

Label 476100.df
Number of curves $2$
Conductor $476100$
CM no
Rank $1$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 476100.df have rank \(1\).

Complex multiplication

The elliptic curves in class 476100.df do not have complex multiplication.

Modular form 476100.2.a.df

Copy content sage:E.q_eigenform(10)
 
\(q + 4 q^{7} + 4 q^{11} - 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 476100.df

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476100.df1 476100df1 \([0, 0, 0, -358800, -82722375]\) \(62200479744/625\) \(51329531250000\) \([2]\) \(2875392\) \(1.7899\) \(\Gamma_0(N)\)-optimal
476100.df2 476100df2 \([0, 0, 0, -350175, -86888250]\) \(-3613864464/390625\) \(-513295312500000000\) \([2]\) \(5750784\) \(2.1365\)