Properties

Label 10830.bb
Number of curves $2$
Conductor $10830$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("10830.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.bb1 10830ba2 [1, 0, 0, -31956, -2203830] [] 38880  
10830.bb2 10830ba1 [1, 0, 0, 534, -14004] [3] 12960 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10830.bb have rank \(1\).

Modular form 10830.2.a.bb

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - q^{10} - 3q^{11} + q^{12} + 2q^{13} - q^{14} - q^{15} + q^{16} - 6q^{17} + q^{18} + O(q^{20}) \)

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.