Properties

Label 102960.bp
Number of curves $2$
Conductor $102960$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 102960.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
102960.bp1 102960de2 \([0, 0, 0, -2398683, -1429926262]\) \(-511157582445795481/8504770560\) \(-25395108815831040\) \([]\) \(1244160\) \(2.2787\)  
102960.bp2 102960de1 \([0, 0, 0, -11883, -4276582]\) \(-62146192681/2610036000\) \(-7793525735424000\) \([]\) \(414720\) \(1.7294\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 102960.bp have rank \(0\).

Complex multiplication

The elliptic curves in class 102960.bp do not have complex multiplication.

Modular form 102960.2.a.bp

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.