Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 16830.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16830.b1 16830s2 \([1, -1, 0, -83565, -6374619]\) \(88526309511756241/26991954000000\) \(19677134466000000\) \([2]\) \(172032\) \(1.8314\)  
16830.b2 16830s1 \([1, -1, 0, 14355, -675675]\) \(448733772344879/527357952000\) \(-384443947008000\) \([2]\) \(86016\) \(1.4848\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 16830.2.a.b

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