Properties

Label 16830.x
Number of curves 4
Conductor 16830
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("16830.x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16830.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.x1 16830bh4 [1, -1, 0, -1605834, 682139340] [6] 663552  
16830.x2 16830bh2 [1, -1, 0, -410274, -100929132] [2] 221184  
16830.x3 16830bh1 [1, -1, 0, -18594, -2460780] [2] 110592 \(\Gamma_0(N)\)-optimal
16830.x4 16830bh3 [1, -1, 0, 162846, 57087828] [6] 331776  

Rank

sage: E.rank()
 

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

Modular form 16830.2.a.x

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.