Properties

Label 272832.o
Number of curves $6$
Conductor $272832$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("272832.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 272832.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
272832.o1 272832o4 [0, -1, 0, -641700929, -6256511805375] [2] 37748736  
272832.o2 272832o5 [0, -1, 0, -133182849, 480959045505] [2] 75497472  
272832.o3 272832o3 [0, -1, 0, -40874689, -93806943551] [2, 2] 37748736  
272832.o4 272832o2 [0, -1, 0, -40106369, -97747656831] [2, 2] 18874368  
272832.o5 272832o1 [0, -1, 0, -2458689, -1587952575] [2] 9437184 \(\Gamma_0(N)\)-optimal
272832.o6 272832o6 [0, -1, 0, 39140351, -416379575807] [2] 75497472  

Rank

sage: E.rank()
 

The elliptic curves in class 272832.o have rank \(0\).

Modular form 272832.2.a.o

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{5} + q^{9} - 4q^{11} - 2q^{13} + 2q^{15} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.