Properties

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

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Show commands: SageMath
E = EllipticCurve("bv1")
 
E.isogeny_class()
 

Elliptic curves in class 5760.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5760.bv1 5760bu1 [0,0,0,5457,152494][0, 0, 0, -5457, 152494] 192596360288/3796875192596360288/3796875 354294000000354294000000 [2][2] 76807680 1.00821.0082 Γ0(N)\Gamma_0(N)-optimal
5760.bv2 5760bu2 [0,0,0,168,451744][0, 0, 0, 168, 451744] 43904/738112543904/7381125 88159684608000-88159684608000 [2][2] 1536015360 1.35471.3547  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5760.2.a.bv

sage: E.q_eigenform(10)
 
q+q5+4q7+2q11+O(q20)q + q^{5} + 4 q^{7} + 2 q^{11} + 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.