Properties

Label 10830.e
Number of curves 4
Conductor 10830
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("10830.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.e1 10830e4 [1, 1, 0, -167226398, -531563735292] [2] 6220800  
10830.e2 10830e2 [1, 1, 0, -149811758, -705838483788] [2] 2073600  
10830.e3 10830e1 [1, 1, 0, -9339438, -11090483532] [2] 1036800 \(\Gamma_0(N)\)-optimal
10830.e4 10830e3 [1, 1, 0, 30861522, -57697813068] [2] 3110400  

Rank

sage: E.rank()
 

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

Modular form 10830.2.a.e

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

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.