Properties

Label 5200.j
Number of curves 11
Conductor 52005200
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 5200.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5200.j1 5200y1 [0,1,0,4792,1411088][0, -1, 0, 4792, -1411088] 304175/21632304175/21632 865280000000000-865280000000000 [][] 2016020160 1.54571.5457 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5200.j1 has rank 11.

Complex multiplication

The elliptic curves in class 5200.j do not have complex multiplication.

Modular form 5200.2.a.j

sage: E.q_eigenform(10)
 
qq34q72q9q11+q13+7q17+3q19+O(q20)q - q^{3} - 4 q^{7} - 2 q^{9} - q^{11} + q^{13} + 7 q^{17} + 3 q^{19} + O(q^{20}) Copy content Toggle raw display