Properties

Label 130130h
Number of curves 4
Conductor 130130
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("130130.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 130130h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
130130.h3 130130h1 [1, 0, 1, -9468, 6899258] [2] 1244160 \(\Gamma_0(N)\)-optimal
130130.h2 130130h2 [1, 0, 1, -604348, 179176506] [2] 2488320  
130130.h4 130130h3 [1, 0, 1, 85172, -185863494] [2] 3732480  
130130.h1 130130h4 [1, 0, 1, -4413608, -3468173382] [2] 7464960  

Rank

sage: E.rank()
 

The elliptic curves in class 130130h have rank \(1\).

Modular form 130130.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{2} - 2q^{3} + q^{4} + q^{5} + 2q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + q^{11} - 2q^{12} + q^{14} - 2q^{15} + q^{16} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.