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Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 16830.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16830.j1 16830g2 \([1, -1, 0, -3120, -66250]\) \(170676802323/158950\) \(3128612850\) \([2]\) \(18432\) \(0.74478\)  
16830.j2 16830g1 \([1, -1, 0, -150, -1504]\) \(-19034163/41140\) \(-809758620\) \([2]\) \(9216\) \(0.39820\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 16830.2.a.j

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