Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("10830.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.k3 10830l1 [1, 0, 1, -11199, -454334] [2] 23040 \(\Gamma_0(N)\)-optimal
10830.k2 10830l2 [1, 0, 1, -18419, 201242] [2, 2] 46080  
10830.k1 10830l3 [1, 0, 1, -224189, 40779086] [2] 92160  
10830.k4 10830l4 [1, 0, 1, 71831, 1609142] [2] 92160  

Rank

sage: E.rank()
 

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

Modular form 10830.2.a.k

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

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.