Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("160080.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 160080bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
160080.l1 160080bx1 [0, -1, 0, -5976, -175824] [2] 110592 \(\Gamma_0(N)\)-optimal
160080.l2 160080bx2 [0, -1, 0, -5576, -200784] [2] 221184  

Rank

sage: E.rank()
 

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

Modular form 160080.2.a.l

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} - 2q^{11} + 2q^{13} + q^{15} - 4q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.