Properties

Label 162288o
Number of curves $6$
Conductor $162288$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("162288.bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162288o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162288.bg5 162288o1 [0, 0, 0, 888909, -660679054] [2] 4718592 \(\Gamma_0(N)\)-optimal
162288.bg4 162288o2 [0, 0, 0, -8142771, -7653005710] [2, 2] 9437184  
162288.bg3 162288o3 [0, 0, 0, -35802291, 75021299570] [2, 2] 18874368  
162288.bg2 162288o4 [0, 0, 0, -124990131, -537836216974] [2] 18874368  
162288.bg1 162288o5 [0, 0, 0, -558369651, 5078394744626] [2] 37748736  
162288.bg6 162288o6 [0, 0, 0, 44212749, 362803392434] [2] 37748736  

Rank

sage: E.rank()
 

The elliptic curves in class 162288o have rank \(0\).

Modular form 162288.2.a.bg

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

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.