Properties

Label 476850.il
Number of curves $1$
Conductor $476850$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("il1")
 
E.isogeny_class()
 

Elliptic curves in class 476850.il

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476850.il1 476850il1 \([1, 0, 0, -664255813, -17873188376383]\) \(-85944135790429956649/316171526414008320\) \(-119243938041460131102720000000\) \([]\) \(507617280\) \(4.2650\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 476850.il1 has rank \(1\).

Complex multiplication

The elliptic curves in class 476850.il do not have complex multiplication.

Modular form 476850.2.a.il

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - 3 q^{7} + q^{8} + q^{9} - q^{11} + q^{12} - q^{13} - 3 q^{14} + q^{16} + q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display