Properties

Label 11968.s
Number of curves 11
Conductor 1196811968
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 11968.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11968.s1 11968j1 [0,1,0,5,349][0, 1, 0, -5, -349] 1024/3179-1024/3179 52084736-52084736 [][] 20482048 0.159640.15964 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 11968.s1 has rank 11.

Complex multiplication

The elliptic curves in class 11968.s do not have complex multiplication.

Modular form 11968.2.a.s

sage: E.q_eigenform(10)
 
q+q3+q5+2q72q9+q112q13+q15+q17+2q19+O(q20)q + q^{3} + q^{5} + 2 q^{7} - 2 q^{9} + q^{11} - 2 q^{13} + q^{15} + q^{17} + 2 q^{19} + O(q^{20}) Copy content Toggle raw display