Properties

Label 117600df
Number of curves $4$
Conductor $117600$
CM no
Rank $1$
Graph

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

Elliptic curves in class 117600df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117600.er3 117600df1 \([0, 1, 0, -24826258, 47474097488]\) \(14383655824793536/45209390625\) \(5318839597640625000000\) \([2, 2]\) \(8847360\) \(3.0360\) \(\Gamma_0(N)\)-optimal
117600.er4 117600df2 \([0, 1, 0, -14407633, 87637896863]\) \(-43927191786304/415283203125\) \(-3126889828125000000000000\) \([2]\) \(17694720\) \(3.3826\)  
117600.er2 117600df3 \([0, 1, 0, -35545008, 2476784988]\) \(5276930158229192/3050936350875\) \(2871516885952743000000000\) \([2]\) \(17694720\) \(3.3826\)  
117600.er1 117600df4 \([0, 1, 0, -396920008, 3043572972488]\) \(7347751505995469192/72930375\) \(68641485507000000000\) \([2]\) \(17694720\) \(3.3826\)  

Rank

sage: E.rank()
 

The elliptic curves in class 117600df have rank \(1\).

Complex multiplication

The elliptic curves in class 117600df do not have complex multiplication.

Modular form 117600.2.a.df

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 4 q^{11} - 2 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.