Properties

Label 5929.h
Number of curves $3$
Conductor $5929$
CM no
Rank $1$
Graph

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

Elliptic curves in class 5929.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5929.h1 5929h3 \([0, 1, 1, -46366756, -121538372763]\) \(-52893159101157376/11\) \(-2292646180979\) \([]\) \(216000\) \(2.6686\)  
5929.h2 5929h2 \([0, 1, 1, -61266, -10592543]\) \(-122023936/161051\) \(-33566632735713539\) \([]\) \(43200\) \(1.8639\)  
5929.h3 5929h1 \([0, 1, 1, -1976, 79657]\) \(-4096/11\) \(-2292646180979\) \([]\) \(8640\) \(1.0592\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5929.h have rank \(1\).

Complex multiplication

The elliptic curves in class 5929.h do not have complex multiplication.

Modular form 5929.2.a.h

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

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.