Properties

Label 92736fj
Number of curves $2$
Conductor $92736$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("fj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92736fj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92736.da2 92736fj1 \([0, 0, 0, -1020, 16112]\) \(-9826000/3703\) \(-44228395008\) \([2]\) \(61440\) \(0.75255\) \(\Gamma_0(N)\)-optimal
92736.da1 92736fj2 \([0, 0, 0, -17580, 897104]\) \(12576878500/1127\) \(53843263488\) \([2]\) \(122880\) \(1.0991\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92736fj have rank \(1\).

Complex multiplication

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

Modular form 92736.2.a.fj

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