Properties

Label 236992.be
Number of curves $2$
Conductor $236992$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.be1 236992be2 \([0, 0, 0, -8064076, 8786520720]\) \(1494447319737/5411854\) \(210016303324386033664\) \([2]\) \(9732096\) \(2.7605\)  
236992.be2 236992be1 \([0, 0, 0, -277196, 261444496]\) \(-60698457/725788\) \(-28165451757789380608\) \([2]\) \(4866048\) \(2.4139\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 236992.be have rank \(0\).

Complex multiplication

The elliptic curves in class 236992.be do not have complex multiplication.

Modular form 236992.2.a.be

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.