Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221067.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.r1 221067t1 \([0, 0, 1, -1452, 4144]\) \(31719424/17661\) \(188500957029\) \([]\) \(139776\) \(0.85387\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 221067.r1 has rank \(1\).

Complex multiplication

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

Modular form 221067.2.a.r

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