Properties

Label 38962be
Number of curves $2$
Conductor $38962$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 38962be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38962.be2 38962be1 \([1, 0, 0, -37694, 2461592]\) \(3343374301177/453439756\) \(803296187579116\) \([]\) \(195840\) \(1.5872\) \(\Gamma_0(N)\)-optimal
38962.be1 38962be2 \([1, 0, 0, -2945929, 1945927897]\) \(1596005697643892137/5553856\) \(9838994689216\) \([]\) \(587520\) \(2.1365\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38962be have rank \(0\).

Complex multiplication

The elliptic curves in class 38962be do not have complex multiplication.

Modular form 38962.2.a.be

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