Properties

Label 200277.w
Number of curves $1$
Conductor $200277$
CM no
Rank $1$

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

Elliptic curves in class 200277.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
200277.w1 200277w1 \([1, -1, 0, -25263567, -48839419310]\) \(350662100640625/246071287\) \(1251353002642581797343\) \([]\) \(14688000\) \(2.9845\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 200277.w1 has rank \(1\).

Complex multiplication

The elliptic curves in class 200277.w do not have complex multiplication.

Modular form 200277.2.a.w

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