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Properties

Label 10830.j
Number of curves $2$
Conductor $10830$
CM no
Rank $0$
Graph

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

Elliptic curves in class 10830.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.j1 10830i1 \([1, 0, 1, -13004, 656102]\) \(-14317849/2700\) \(-45855620210700\) \([3]\) \(49248\) \(1.3455\) \(\Gamma_0(N)\)-optimal
10830.j2 10830i2 \([1, 0, 1, 89881, -3212374]\) \(4728305591/3000000\) \(-50950689123000000\) \([]\) \(147744\) \(1.8948\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10830.j have rank \(0\).

Complex multiplication

The elliptic curves in class 10830.j do not have complex multiplication.

Modular form 10830.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + 6 q^{11} + q^{12} + 5 q^{13} + q^{14} - q^{15} + q^{16} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.