Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("16830.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16830.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.h1 16830k2 [1, -1, 0, -7710, -318700] [] 43200  
16830.h2 16830k1 [1, -1, 0, 705, 3501] [3] 14400 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 16830.2.a.h

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

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.