Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16830.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.cd1 16830ck2 [1, -1, 1, -1292, -11091] [2] 16384  
16830.cd2 16830ck1 [1, -1, 1, 238, -1299] [2] 8192 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 16830.cd do not have complex multiplication.

Modular form 16830.2.a.cd

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

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.