Properties

Label 115920.ee
Number of curves $2$
Conductor $115920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ee1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.ee

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ee1 115920cs1 \([0, 0, 0, -66387, 6417234]\) \(292583028222603/8456021875\) \(935168371200000\) \([2]\) \(552960\) \(1.6506\) \(\Gamma_0(N)\)-optimal
115920.ee2 115920cs2 \([0, 0, 0, 15933, 21284226]\) \(4044759171237/1771943359375\) \(-195962760000000000\) \([2]\) \(1105920\) \(1.9972\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.ee have rank \(1\).

Complex multiplication

The elliptic curves in class 115920.ee do not have complex multiplication.

Modular form 115920.2.a.ee

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{7} - 4q^{11} + 4q^{13} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.