Properties

Label 236992.cm
Number of curves $2$
Conductor $236992$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992.cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.cm1 236992cm2 \([0, -1, 0, -17633, 517793]\) \(125000/49\) \(237691160526848\) \([2]\) \(720896\) \(1.4571\)  
236992.cm2 236992cm1 \([0, -1, 0, 3527, 56505]\) \(8000/7\) \(-4244485009408\) \([2]\) \(360448\) \(1.1105\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 236992.2.a.cm

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