Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 43560.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43560.e1 43560e1 [0,0,0,290763,60158538][0, 0, 0, -290763, -60158538] 76136652/27576136652/275 98192892619008009819289261900800 [2][2] 460800460800 1.92971.9297 Γ0(N)\Gamma_0(N)-optimal
43560.e2 43560e2 [0,0,0,160083,114495282][0, 0, 0, -160083, -114495282] 6353046/75625-6353046/75625 5400609094045440000-5400609094045440000 [2][2] 921600921600 2.27632.2763  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 43560.2.a.e

sage: E.q_eigenform(10)
 
qq54q7+4q132q17+6q19+O(q20)q - q^{5} - 4 q^{7} + 4 q^{13} - 2 q^{17} + 6 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.