Properties

Label 92736fq
Number of curves $4$
Conductor $92736$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fq1")
 
E.isogeny_class()
 

Elliptic curves in class 92736fq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92736.bj4 92736fq1 \([0, 0, 0, -345036, -127251056]\) \(-23771111713777/22848457968\) \(-4366408314695712768\) \([2]\) \(1474560\) \(2.2729\) \(\Gamma_0(N)\)-optimal
92736.bj3 92736fq2 \([0, 0, 0, -6439116, -6287147120]\) \(154502321244119857/55101928644\) \(10530142547208044544\) \([2, 2]\) \(2949120\) \(2.6194\)  
92736.bj2 92736fq3 \([0, 0, 0, -7366476, -4357867376]\) \(231331938231569617/90942310746882\) \(17379346228045932920832\) \([2]\) \(5898240\) \(2.9660\)  
92736.bj1 92736fq4 \([0, 0, 0, -103017036, -402449774960]\) \(632678989847546725777/80515134\) \(15386681720438784\) \([2]\) \(5898240\) \(2.9660\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92736.2.a.fq

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + q^{7} - 4 q^{11} - 2 q^{13} - 6 q^{17} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.