Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221067.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221067.f1 221067d1 [1, -1, 1, -23, -424542] [] 414720 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 221067.f1 has rank \(1\).

Complex multiplication

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

Modular form 221067.2.a.f

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