Properties

Label 100016.a
Number of curves 2
Conductor 100016
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("100016.a1")
sage: E.isogeny_class()

Elliptic curves in class 100016.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100016.a1 100016a1 [0, 1, 0, -84, -164] 2 19712 \(\Gamma_0(N)\)-optimal
100016.a2 100016a2 [0, 1, 0, 296, -924] 2 39424  

Rank

sage: E.rank()

The elliptic curves in class 100016.a have rank \(1\).

Modular form 100016.2.a.a

sage: E.q_eigenform(10)
\( q - 2q^{3} - 2q^{5} - q^{7} + q^{9} + 2q^{13} + 4q^{15} + 6q^{17} - q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.