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 order 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.