Properties

Label 166635.w
Number of curves $1$
Conductor $166635$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 166635.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166635.w1 166635be1 \([0, 0, 1, -88989438, 321545214508]\) \(2580674412544/14467005\) \(436902490203243374257605\) \([]\) \(19783680\) \(3.3784\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 166635.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 166635.w do not have complex multiplication.

Modular form 166635.2.a.w

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - q^{5} - q^{7} + 3 q^{11} - 6 q^{13} + 4 q^{16} + 4 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display