Properties

Label 208725.i
Number of curves 11
Conductor 208725208725
CM no
Rank 11

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 208725.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
208725.i1 208725b1 [0,1,1,458,31994][0, 1, 1, -458, 31994] 45056/1863-45056/1863 440279296875-440279296875 [][] 395520395520 0.914340.91434 Γ0(N)\Gamma_0(N)-optimal

Rank

sage: E.rank()
 

The elliptic curve 208725.i1 has rank 11.

Complex multiplication

The elliptic curves in class 208725.i do not have complex multiplication.

Modular form 208725.2.a.i

sage: E.q_eigenform(10)
 
q2q2+q3+2q42q6+q7+q9+2q124q132q144q163q172q18+6q19+O(q20)q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{6} + q^{7} + q^{9} + 2 q^{12} - 4 q^{13} - 2 q^{14} - 4 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + O(q^{20}) Copy content Toggle raw display