Properties

Label 92736cj
Number of curves $2$
Conductor $92736$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92736cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92736.dn2 92736cj1 \([0, 0, 0, 19860, -5067344]\) \(4533086375/60669952\) \(-11594208380977152\) \([2]\) \(516096\) \(1.7632\) \(\Gamma_0(N)\)-optimal
92736.dn1 92736cj2 \([0, 0, 0, -348780, -74224208]\) \(24553362849625/1755162752\) \(335416825271549952\) \([2]\) \(1032192\) \(2.1098\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92736cj have rank \(0\).

Complex multiplication

The elliptic curves in class 92736cj do not have complex multiplication.

Modular form 92736.2.a.cj

sage: E.q_eigenform(10)
 
\(q + q^{7} + 4q^{11} - 6q^{17} + 6q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.