Properties

Label 43560.bz
Number of curves 22
Conductor 4356043560
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 43560.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43560.bz1 43560cd2 [0,0,0,1947,32186][0, 0, 0, -1947, -32186] 821516/25821516/25 2483965440024839654400 [2][2] 2764827648 0.770720.77072  
43560.bz2 43560cd1 [0,0,0,33,1694][0, 0, 0, 33, -1694] 16/516/5 1241982720-1241982720 [2][2] 1382413824 0.424140.42414 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43560.bz have rank 00.

Complex multiplication

The elliptic curves in class 43560.bz do not have complex multiplication.

Modular form 43560.2.a.bz

sage: E.q_eigenform(10)
 
q+q5+2q13+6q17+O(q20)q + q^{5} + 2 q^{13} + 6 q^{17} + 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.