Properties

Label 10830g
Number of curves 4
Conductor 10830
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("10830.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.g4 10830g1 [1, 1, 0, 3369928, 5064449856] [2] 864000 \(\Gamma_0(N)\)-optimal
10830.g3 10830g2 [1, 1, 0, -31748152, 59307836224] [2] 1728000  
10830.g2 10830g3 [1, 1, 0, -1191828872, 15836364428016] [2] 4320000  
10830.g1 10830g4 [1, 1, 0, -19069263652, 1013550971091124] [2] 8640000  

Rank

sage: E.rank()
 

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

Modular form 10830.2.a.g

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.