Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("16830.cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16830.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.cp1 16830br2 [1, -1, 1, -347, 2569] [2] 6144  
16830.cp2 16830br1 [1, -1, 1, -17, 61] [2] 3072 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 16830.2.a.cp

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + q^{11} + 6q^{13} + q^{16} - q^{17} - 4q^{19} + O(q^{20}) \)

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 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.