Properties

Label 236992.ce
Number of curves $2$
Conductor $236992$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.ce1 236992ce2 \([0, -1, 0, -1151809, -461125695]\) \(1431644/49\) \(5783976700260319232\) \([2]\) \(3956736\) \(2.3720\)  
236992.ce2 236992ce1 \([0, -1, 0, -178449, 19130129]\) \(21296/7\) \(206570596437868544\) \([2]\) \(1978368\) \(2.0254\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 236992.2.a.ce

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