Properties

Label 100010f
Number of curves 2
Conductor 100010
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("100010.j1")
sage: E.isogeny_class()

Elliptic curves in class 100010f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100010.j2 100010f1 [1, 1, 1, -120, 245] 2 45056 \(\Gamma_0(N)\)-optimal
100010.j1 100010f2 [1, 1, 1, -850, -9683] 2 90112  

Rank

sage: E.rank()

The elliptic curves in class 100010f have rank \(1\).

Modular form None

sage: E.q_eigenform(10)
\( q + q^{2} + 2q^{3} + q^{4} + q^{5} + 2q^{6} - 4q^{7} + q^{8} + q^{9} + q^{10} + 4q^{11} + 2q^{12} - 2q^{13} - 4q^{14} + 2q^{15} + q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.