Properties

Label 16830s
Number of curves 2
Conductor 16830
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("16830.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16830s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.b2 16830s1 [1, -1, 0, 14355, -675675] [2] 86016 \(\Gamma_0(N)\)-optimal
16830.b1 16830s2 [1, -1, 0, -83565, -6374619] [2] 172032  

Rank

sage: E.rank()
 

The elliptic curves in class 16830s have rank \(1\).

Modular form 16830.2.a.b

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

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.