Properties

Label 46800.df
Number of curves $4$
Conductor $46800$
CM no
Rank $0$
Graph

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

Elliptic curves in class 46800.df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.df1 46800o4 \([0, 0, 0, -1308675, 576049250]\) \(10625310339698/3855735\) \(89946586080000000\) \([2]\) \(589824\) \(2.2217\)  
46800.df2 46800o3 \([0, 0, 0, -678675, -210820750]\) \(1481943889298/34543665\) \(805834617120000000\) \([2]\) \(589824\) \(2.2217\)  
46800.df3 46800o2 \([0, 0, 0, -93675, 6214250]\) \(7793764996/3080025\) \(35925411600000000\) \([2, 2]\) \(294912\) \(1.8751\)  
46800.df4 46800o1 \([0, 0, 0, 18825, 701750]\) \(253012016/219375\) \(-639697500000000\) \([2]\) \(147456\) \(1.5285\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46800.df have rank \(0\).

Complex multiplication

The elliptic curves in class 46800.df do not have complex multiplication.

Modular form 46800.2.a.df

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.