Properties

Label 9360bn
Number of curves $6$
Conductor $9360$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9360.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9360bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9360.p6 9360bn1 [0, 0, 0, 2157, 15442] [2] 12288 \(\Gamma_0(N)\)-optimal
9360.p5 9360bn2 [0, 0, 0, -9363, 128338] [2, 2] 24576  
9360.p3 9360bn3 [0, 0, 0, -81363, -8842862] [2, 2] 49152  
9360.p2 9360bn4 [0, 0, 0, -121683, 16324882] [2] 49152  
9360.p1 9360bn5 [0, 0, 0, -1298163, -569300942] [2] 98304  
9360.p4 9360bn6 [0, 0, 0, -16563, -22541582] [2] 98304  

Rank

sage: E.rank()
 

The elliptic curves in class 9360bn have rank \(0\).

Modular form 9360.2.a.p

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

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.