Properties

Label 236992.p
Number of curves $2$
Conductor $236992$
CM no
Rank $0$
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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 236992.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.p1 236992p2 \([0, 1, 0, -35904993, 12061596319]\) \(263822189935250/149429406721\) \(2899432579620642484256768\) \([2]\) \(32440320\) \(3.3838\)  
236992.p2 236992p1 \([0, 1, 0, 8869567, 1503755071]\) \(7953970437500/4703287687\) \(-45629792188353658421248\) \([2]\) \(16220160\) \(3.0373\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 236992.2.a.p

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