Properties

Label 100014f
Number of curves 2
Conductor 100014
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("100014.e1")
sage: E.isogeny_class()

Elliptic curves in class 100014f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100014.e2 100014f1 [1, 0, 0, -11707, 482009] 3 404640 \(\Gamma_0(N)\)-optimal
100014.e1 100014f2 [1, 0, 0, -87037, -9623389] 1 1213920  

Rank

sage: E.rank()

The elliptic curves in class 100014f have rank \(1\).

Modular form 100014.2.a.e

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

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.