Properties

Label 221067.x
Number of curves $1$
Conductor $221067$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 221067.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.x1 221067x1 \([1, -1, 0, -2588031, -1603683284]\) \(-1484391946907017/1946200179\) \(-2513455192440566451\) \([]\) \(5760000\) \(2.4375\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 221067.x1 has rank \(0\).

Complex multiplication

The elliptic curves in class 221067.x do not have complex multiplication.

Modular form 221067.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 3 q^{5} - q^{7} - 3 q^{8} - 3 q^{10} + 3 q^{13} - q^{14} - q^{16} + q^{17} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display