Properties

Label 38720df
Number of curves $2$
Conductor $38720$
CM no
Rank $0$
Graph

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

Elliptic curves in class 38720df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38720.cs1 38720df1 \([0, 1, 0, -7905, 736415]\) \(-117649/440\) \(-204337798184960\) \([]\) \(92160\) \(1.4316\) \(\Gamma_0(N)\)-optimal
38720.cs2 38720df2 \([0, 1, 0, 69535, -17523937]\) \(80062991/332750\) \(-154530459877376000\) \([]\) \(276480\) \(1.9809\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38720df have rank \(0\).

Complex multiplication

The elliptic curves in class 38720df do not have complex multiplication.

Modular form 38720.2.a.df

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} - 2 q^{9} + 2 q^{13} + q^{15} + 3 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.