Properties

Label 188760.bq
Number of curves $2$
Conductor $188760$
CM no
Rank $0$
Graph

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

Elliptic curves in class 188760.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.bq1 188760bb2 \([0, -1, 0, -2587020, -1596035868]\) \(3172116339056/10710375\) \(6465153024254496000\) \([2]\) \(5068800\) \(2.4735\)  
188760.bq2 188760bb1 \([0, -1, 0, -91395, -46751868]\) \(-2237904896/23765625\) \(-896609609502750000\) \([2]\) \(2534400\) \(2.1269\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 188760.bq have rank \(0\).

Complex multiplication

The elliptic curves in class 188760.bq do not have complex multiplication.

Modular form 188760.2.a.bq

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