Properties

Label 348726o
Number of curves $6$
Conductor $348726$
CM no
Rank $0$
Graph

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

Elliptic curves in class 348726o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
348726.o6 348726o1 [1, 0, 1, -3619030062, 615395366299744] [2] 1455390720 \(\Gamma_0(N)\)-optimal
348726.o5 348726o2 [1, 0, 1, -132927959342, 18561302360351840] [2, 2] 2910781440  
348726.o2 348726o3 [1, 0, 1, -2123909643262, 1191384900943738400] [2, 2] 5821562880  
348726.o4 348726o4 [1, 0, 1, -210889143902, -5723731367983456] [2] 5821562880  
348726.o1 348726o5 [1, 0, 1, -33982554021322, 76248643432314434384] [2] 11643125760  
348726.o3 348726o6 [1, 0, 1, -2120972207922, 1194844642836517936] [2] 11643125760  

Rank

sage: E.rank()
 

The elliptic curves in class 348726o have rank \(0\).

Complex multiplication

The elliptic curves in class 348726o do not have complex multiplication.

Modular form 348726.2.a.o

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - 2q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} - 4q^{11} + q^{12} + 2q^{13} + q^{14} - 2q^{15} + q^{16} - 6q^{17} - q^{18} + O(q^{20}) \)

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.