Properties

Label 221067.w
Number of curves $1$
Conductor $221067$
CM no
Rank $2$

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

Elliptic curves in class 221067.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.w1 221067v1 \([0, 0, 1, -264, -10112]\) \(-23068672/487403\) \(-42993331227\) \([]\) \(144000\) \(0.72122\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 221067.w1 has rank \(2\).

Complex multiplication

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

Modular form 221067.2.a.w

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