Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.cb1 236992cb2 \([0, -1, 0, -85345, -9452799]\) \(3543122/49\) \(950764642107392\) \([2]\) \(1441792\) \(1.6797\)  
236992.cb2 236992cb1 \([0, -1, 0, -705, -396319]\) \(-4/7\) \(-67911760150528\) \([2]\) \(720896\) \(1.3331\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 236992.2.a.cb

sage: E.q_eigenform(10)
 
\(q + 2q^{3} - 4q^{5} + q^{7} + q^{9} - 8q^{15} + 2q^{17} + 2q^{19} + O(q^{20})\)  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.