Properties

Label 16830.e
Number of curves 2
Conductor 16830
CM no
Rank 2
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("16830.e1")
sage: E.isogeny_class()

Elliptic curves in class 16830.e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
16830.e1 16830q2 [1, -1, 0, -7920, -244904] 2 36864  
16830.e2 16830q1 [1, -1, 0, -1800, 25600] 2 18432 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 16830.e have rank \(2\).

Modular form 16830.2.a.e

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

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.