Properties

Label 7360.o
Number of curves 44
Conductor 73607360
CM no
Rank 00
Graph

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

Elliptic curves in class 7360.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7360.o1 7360y3 [0,0,0,1772,17136][0, 0, 0, -1772, 17136] 18778674312/699602518778674312/6996025 229245747200229245747200 [4][4] 56325632 0.879710.87971  
7360.o2 7360y2 [0,0,0,772,8064][0, 0, 0, -772, -8064] 12422690496/33062512422690496/330625 13542400001354240000 [2,2][2, 2] 28162816 0.533130.53313  
7360.o3 7360y1 [0,0,0,767,8176][0, 0, 0, -767, -8176] 779704121664/575779704121664/575 3680036800 [2][2] 14081408 0.186560.18656 Γ0(N)\Gamma_0(N)-optimal
7360.o4 7360y4 [0,0,0,148,26096][0, 0, 0, 148, -26096] 10941048/898437510941048/8984375 294400000000-294400000000 [2][2] 56325632 0.879710.87971  

Rank

sage: E.rank()
 

The elliptic curves in class 7360.o have rank 00.

Complex multiplication

The elliptic curves in class 7360.o do not have complex multiplication.

Modular form 7360.2.a.o

sage: E.q_eigenform(10)
 
q+q53q94q11+2q13+2q17+4q19+O(q20)q + q^{5} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The i,ji,j entry is the smallest degree of a cyclic isogeny between the ii-th and jj-th curve in the isogeny class, in the LMFDB numbering.

(1244212242144241)\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.