Properties

Label 640.e
Number of curves 22
Conductor 640640
CM no
Rank 11
Graph

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

Elliptic curves in class 640.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
640.e1 640g2 [0,0,0,52,144][0, 0, 0, -52, 144] 1898208/51898208/5 4096040960 [2][2] 6464 0.23996-0.23996  
640.e2 640g1 [0,0,0,2,4][0, 0, 0, -2, 4] 3456/25-3456/25 6400-6400 [2][2] 3232 0.58654-0.58654 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 640.e have rank 11.

Complex multiplication

The elliptic curves in class 640.e do not have complex multiplication.

Modular form 640.2.a.e

sage: E.q_eigenform(10)
 
q+q52q73q96q11+2q136q17+2q19+O(q20)q + q^{5} - 2 q^{7} - 3 q^{9} - 6 q^{11} + 2 q^{13} - 6 q^{17} + 2 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.