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Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 16830k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16830.h2 16830k1 \([1, -1, 0, 705, 3501]\) \(1434104310933/1046272480\) \(-28249356960\) \([3]\) \(14400\) \(0.69368\) \(\Gamma_0(N)\)-optimal
16830.h1 16830k2 \([1, -1, 0, -7710, -318700]\) \(-2575296504243/765952000\) \(-15076233216000\) \([]\) \(43200\) \(1.2430\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 16830.2.a.k

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.