Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("10830.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.p4 10830p1 [1, 0, 1, -685908, -228577454] [2] 345600 \(\Gamma_0(N)\)-optimal
10830.p3 10830p2 [1, 0, 1, -11111588, -14257372462] [2, 2] 691200  
10830.p1 10830p3 [1, 0, 1, -177785288, -912428607022] [2] 1382400  
10830.p2 10830p4 [1, 0, 1, -11248768, -13887315694] [4] 1382400  

Rank

sage: E.rank()
 

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

Modular form 10830.2.a.p

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.