Properties

Label 16830o
Number of curves 4
Conductor 16830
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("16830.w1")
sage: E.isogeny_class()

Elliptic curves in class 16830o

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
16830.w4 16830o1 [1, -1, 0, -4209, -8344035] 6 161280 \(\Gamma_0(N)\)-optimal
16830.w3 16830o2 [1, -1, 0, -643089, -195791427] 6 322560  
16830.w2 16830o3 [1, -1, 0, -3243984, -2248180480] 2 483840  
16830.w1 16830o4 [1, -1, 0, -51904464, -143918301952] 2 967680  

Rank

sage: E.rank()

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

Modular form 16830.2.a.w

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.