Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("10830.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10830.h4 10830h1 [1, 1, 0, -3617, -144411] [2] 34560 \(\Gamma_0(N)\)-optimal
10830.h3 10830h2 [1, 1, 0, -68597, -6941319] [2, 2] 69120  
10830.h1 10830h3 [1, 1, 0, -1097447, -442967949] [2] 138240  
10830.h2 10830h4 [1, 1, 0, -79427, -4617201] [2] 138240  

Rank

sage: E.rank()
 

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

Modular form 10830.2.a.h

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

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.