Properties

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

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 16830.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16830.p1 16830c1 \([1, -1, 0, -3255, 61325]\) \(193802978403/31790000\) \(625722570000\) \([2]\) \(36864\) \(0.98519\) \(\Gamma_0(N)\)-optimal
16830.p2 16830c2 \([1, -1, 0, 5925, 338561]\) \(1168574089437/3214062500\) \(-63262392187500\) \([2]\) \(73728\) \(1.3318\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 16830.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} + 2 q^{7} - q^{8} + q^{10} - q^{11} - 6 q^{13} - 2 q^{14} + q^{16} - q^{17} + 4 q^{19} + O(q^{20})\) 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.