Properties

Label 5760.br
Number of curves 22
Conductor 57605760
CM no
Rank 00
Graph

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Copy content sage:E = EllipticCurve("br1") E.isogeny_class()
 

Elliptic curves in class 5760.br

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5760.br1 5760bo2 [0,0,0,372,1424][0, 0, 0, -372, 1424] 953312/405953312/405 24186470402418647040 [2][2] 20482048 0.497210.49721  
5760.br2 5760bo1 [0,0,0,78,164][0, 0, 0, 78, 164] 281216/225281216/225 41990400-41990400 [2][2] 10241024 0.150640.15064 Γ0(N)\Gamma_0(N)-optimal

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 5760.br have rank 00.

Complex multiplication

The elliptic curves in class 5760.br do not have complex multiplication.

Modular form 5760.2.a.br

Copy content sage:E.q_eigenform(10)
 
q+q5+2q7+2q112q13+2q17+2q19+O(q20)q + q^{5} + 2 q^{7} + 2 q^{11} - 2 q^{13} + 2 q^{17} + 2 q^{19} + O(q^{20}) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

(1221)\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.