Properties

Label 10010h
Number of curves 2
Conductor 10010
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("10010.b1")
sage: E.isogeny_class()

Elliptic curves in class 10010h

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
10010.b2 10010h1 [1, 0, 1, -183, -934] 2 3840 \(\Gamma_0(N)\)-optimal
10010.b1 10010h2 [1, 0, 1, -463, 2538] 2 7680  

Rank

sage: E.rank()

The elliptic curves in class 10010h have rank \(1\).

Modular form 10010.2.a.b

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

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.