Properties

Label 3840.bb
Number of curves 22
Conductor 38403840
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 3840.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3840.bb1 3840z2 [0,1,0,365,2037][0, 1, 0, -365, -2037] 164566592/46875164566592/46875 15360000001536000000 [2][2] 15361536 0.469360.46936  
3840.bb2 3840z1 [0,1,0,335,2475][0, 1, 0, -335, -2475] 8144865728/11258144865728/1125 576000576000 [2][2] 768768 0.122790.12279 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3840.bb have rank 00.

Complex multiplication

The elliptic curves in class 3840.bb do not have complex multiplication.

Modular form 3840.2.a.bb

sage: E.q_eigenform(10)
 
q+q3+q5+2q7+q9+2q11+2q13+q15+4q17+4q19+O(q20)q + q^{3} + q^{5} + 2 q^{7} + q^{9} + 2 q^{11} + 2 q^{13} + q^{15} + 4 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.

(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.