Properties

Label 8016f
Number of curves 2
Conductor 8016
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("8016.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8016f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8016.f2 8016f1 [0, -1, 0, -72, 1008] [2] 3456 \(\Gamma_0(N)\)-optimal
8016.f1 8016f2 [0, -1, 0, -1992, 34800] [2] 6912  

Rank

sage: E.rank()
 

The elliptic curves in class 8016f have rank \(0\).

Modular form 8016.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{5} + 4q^{7} + q^{9} + 4q^{11} - 2q^{15} - 4q^{17} + 4q^{19} + O(q^{20}) \)

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.