Properties

Label 38829.h
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 38829.h

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
38829.h1 38829f6 [1, 1, 0, -1449654, 671203533] 2 322560  
38829.h2 38829f4 [1, 1, 0, -90639, 10450440] 4 161280  
38829.h3 38829f3 [1, 1, 0, -72149, -7444182] 2 161280  
38829.h4 38829f5 [1, 1, 0, -62904, 17001447] 2 322560  
38829.h5 38829f2 [1, 1, 0, -7434, 49815] 4 80640  
38829.h6 38829f1 [1, 1, 0, 1811, 7288] 2 40320 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 38829.h 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.