Properties

Label 16830f
Number of curves 2
Conductor 16830
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("16830.i1")
sage: E.isogeny_class()

Elliptic curves in class 16830f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
16830.i2 16830f1 [1, -1, 0, -9522645, 11099832821] 2 1128960 \(\Gamma_0(N)\)-optimal
16830.i1 16830f2 [1, -1, 0, -20581845, -19518668299] 2 2257920  

Rank

sage: E.rank()

The elliptic curves in class 16830f have rank \(0\).

Modular form 16830.2.a.i

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

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 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.