Properties

Label 221067s
Number of curves $1$
Conductor $221067$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 221067s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.u1 221067s1 \([0, 0, 1, -175692, -5515997]\) \(31719424/17661\) \(333940943935252269\) \([]\) \(1537536\) \(2.0528\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 221067s1 has rank \(1\).

Complex multiplication

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

Modular form 221067.2.a.s

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