Properties

Label 116688k
Number of curves $2$
Conductor $116688$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116688k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116688.a1 116688k1 \([0, -1, 0, -631320, -165133584]\) \(6793805286030262681/1048227429629952\) \(4293539551764283392\) \([2]\) \(3612672\) \(2.2987\) \(\Gamma_0(N)\)-optimal
116688.a2 116688k2 \([0, -1, 0, 1099240, -912735504]\) \(35862531227445945959/108547797844556928\) \(-444611779971305177088\) \([2]\) \(7225344\) \(2.6453\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116688k have rank \(0\).

Complex multiplication

The elliptic curves in class 116688k do not have complex multiplication.

Modular form 116688.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{5} + 2q^{7} + q^{9} - q^{11} - q^{13} + 4q^{15} - q^{17} + 4q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.