Properties

Label 92736co
Number of curves $6$
Conductor $92736$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("92736.bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92736co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92736.bk5 92736co1 [0, 0, 0, 72564, -15409424] [2] 786432 \(\Gamma_0(N)\)-optimal
92736.bk4 92736co2 [0, 0, 0, -664716, -178495760] [2, 2] 1572864  
92736.bk3 92736co3 [0, 0, 0, -2922636, 1749767920] [2, 2] 3145728  
92736.bk2 92736co4 [0, 0, 0, -10203276, -12544284944] [2] 3145728  
92736.bk6 92736co5 [0, 0, 0, 3609204, 8461886704] [2] 6291456  
92736.bk1 92736co6 [0, 0, 0, -45581196, 118446524656] [2] 6291456  

Rank

sage: E.rank()
 

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

Modular form 92736.2.a.bk

sage: E.q_eigenform(10)
 
\( q - 2q^{5} + q^{7} - 4q^{11} + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.