Properties

Label 5712.x
Number of curves 44
Conductor 57125712
CM no
Rank 00
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 5712.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5712.x1 5712j4 [0,1,0,2192,38772][0, 1, 0, -2192, 38772] 569001644066/122451569001644066/122451 250779648250779648 [2][2] 30723072 0.606420.60642  
5712.x2 5712j3 [0,1,0,992,12012][0, 1, 0, -992, -12012] 52767497666/175394152767497666/1753941 35920711683592071168 [2][2] 30723072 0.606420.60642  
5712.x3 5712j2 [0,1,0,152,420][0, 1, 0, -152, 420] 381775972/127449381775972/127449 130507776130507776 [2,2][2, 2] 15361536 0.259850.25985  
5712.x4 5712j1 [0,1,0,28,60][0, 1, 0, 28, 60] 9148592/96399148592/9639 2467584-2467584 [2][2] 768768 0.086725-0.086725 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5712.x have rank 00.

Complex multiplication

The elliptic curves in class 5712.x do not have complex multiplication.

Modular form 5712.2.a.x

sage: E.q_eigenform(10)
 
q+q3+2q5q7+q9+4q11+2q13+2q15q17+4q19+O(q20)q + q^{3} + 2 q^{5} - q^{7} + q^{9} + 4 q^{11} + 2 q^{13} + 2 q^{15} - 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.

(1424412422124421)\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)

Isogeny graph

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

The vertices are labelled with LMFDB labels.