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Properties

Label 388311.h
Number of curves $2$
Conductor $388311$
CM no
Rank $1$
Graph

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

Elliptic curves in class 388311.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388311.h1 388311h2 \([0, 1, 1, -137887947, -623260669948]\) \(-36310462268735488/11647251\) \(-93002428359804796371\) \([]\) \(41658624\) \(3.1920\)  
388311.h2 388311h1 \([0, 1, 1, -1424367, -1143678265]\) \(-40023851008/47544651\) \(-379640483279652981771\) \([3]\) \(13886208\) \(2.6427\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 388311.h have rank \(1\).

Complex multiplication

The elliptic curves in class 388311.h do not have complex multiplication.

Modular form 388311.2.a.h

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.