Properties

Label 160080bp
Number of curves $2$
Conductor $160080$
CM no
Rank $0$
Graph

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

Elliptic curves in class 160080bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160080.a2 160080bp1 \([0, -1, 0, -8941, -321359]\) \(308809465667584/1190845125\) \(304856352000\) \([]\) \(393984\) \(1.0619\) \(\Gamma_0(N)\)-optimal
160080.a1 160080bp2 \([0, -1, 0, -47581, 3759025]\) \(46536484258668544/3286798828125\) \(841420500000000\) \([]\) \(1181952\) \(1.6112\)  

Rank

sage: E.rank()
 

The elliptic curves in class 160080bp have rank \(0\).

Complex multiplication

The elliptic curves in class 160080bp do not have complex multiplication.

Modular form 160080.2.a.bp

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 5 q^{7} + q^{9} + 6 q^{11} - 4 q^{13} + q^{15} + 3 q^{17} - 5 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.