Properties

Label 120666.o
Number of curves $6$
Conductor $120666$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("120666.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 120666.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
120666.o1 120666d6 [1, 1, 0, -2318444079, -42968757113667] [2] 70778880  
120666.o2 120666d4 [1, 1, 0, -145178439, -668749349835] [2, 2] 35389440  
120666.o3 120666d5 [1, 1, 0, -49450079, -1537369342803] [2] 70778880  
120666.o4 120666d2 [1, 1, 0, -15332359, 5801035765] [2, 2] 17694720  
120666.o5 120666d1 [1, 1, 0, -11871239, 15718529013] [2] 8847360 \(\Gamma_0(N)\)-optimal
120666.o6 120666d3 [1, 1, 0, 59135801, 45701075893] [2] 35389440  

Rank

sage: E.rank()
 

The elliptic curves in class 120666.o have rank \(0\).

Modular form 120666.2.a.o

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + 2q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - 2q^{10} - 4q^{11} - q^{12} + q^{14} - 2q^{15} + q^{16} + q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.