Properties

Label 66654.bq
Number of curves $2$
Conductor $66654$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 66654.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66654.bq1 66654bj2 \([1, -1, 1, -2882885, 1764560445]\) \(24553362849625/1755162752\) \(189413940104032758912\) \([2]\) \(2838528\) \(2.6378\)  
66654.bq2 66654bj1 \([1, -1, 1, 164155, 120377661]\) \(4533086375/60669952\) \(-6547389774052442112\) \([2]\) \(1419264\) \(2.2912\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 66654.bq have rank \(0\).

Complex multiplication

The elliptic curves in class 66654.bq do not have complex multiplication.

Modular form 66654.2.a.bq

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} + 4q^{11} - q^{14} + q^{16} + 6q^{17} + 6q^{19} + O(q^{20})\)  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.