Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("100016.g1")
sage: E.isogeny_class()

Elliptic curves in class 100016m

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100016.g1 100016m1 [0, 0, 0, -5171, -142350] 2 80640 \(\Gamma_0(N)\)-optimal
100016.g2 100016m2 [0, 0, 0, -2131, -308334] 2 161280  

Rank

sage: E.rank()

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

Modular form None

sage: E.q_eigenform(10)
\( q - 2q^{5} - q^{7} - 3q^{9} + 2q^{11} - 6q^{13} + 2q^{17} + q^{19} + O(q^{20}) \)

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 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.