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Properties

Label 86394bd
Number of curves $3$
Conductor $86394$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 86394bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86394.u3 86394bd1 \([1, 0, 1, 13065, -15511718]\) \(139233463487/58763045376\) \(-104102319429351936\) \([]\) \(1458000\) \(1.9444\) \(\Gamma_0(N)\)-optimal
86394.u2 86394bd2 \([1, 0, 1, -117615, 419339050]\) \(-101566487155393/42823570577256\) \(-75864567515414216616\) \([]\) \(4374000\) \(2.4938\)  
86394.u1 86394bd3 \([1, 0, 1, -46185945, 120813067582]\) \(-6150311179917589675873/244053849830826\) \(-432356282260147939386\) \([]\) \(13122000\) \(3.0431\)  

Rank

sage: E.rank()
 

The elliptic curves in class 86394bd have rank \(0\).

Complex multiplication

The elliptic curves in class 86394bd do not have complex multiplication.

Modular form 86394.2.a.bd

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 3 q^{10} + q^{12} - 5 q^{13} + q^{14} - 3 q^{15} + q^{16} + q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.