Properties

Label 38829f
Number of curves 6
Conductor 38829
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("38829.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38829f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38829.h6 38829f1 [1, 1, 0, 1811, 7288] [2] 40320 \(\Gamma_0(N)\)-optimal
38829.h5 38829f2 [1, 1, 0, -7434, 49815] [2, 2] 80640  
38829.h3 38829f3 [1, 1, 0, -72149, -7444182] [2] 161280  
38829.h2 38829f4 [1, 1, 0, -90639, 10450440] [2, 2] 161280  
38829.h4 38829f5 [1, 1, 0, -62904, 17001447] [2] 322560  
38829.h1 38829f6 [1, 1, 0, -1449654, 671203533] [2] 322560  

Rank

sage: E.rank()
 

The elliptic curves in class 38829f have rank \(1\).

Modular form 38829.2.a.h

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} + 2q^{5} - q^{6} + q^{7} - 3q^{8} + q^{9} + 2q^{10} + 4q^{11} + q^{12} - 2q^{13} + q^{14} - 2q^{15} - q^{16} - 6q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.