Properties

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

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 221067.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.bc1 221067bi1 \([1, -1, 0, -31785, -3858068]\) \(-74246873427/92019697\) \(-4401499673799459\) \([]\) \(898560\) \(1.6952\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 221067.bc1 has rank \(1\).

Complex multiplication

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

Modular form 221067.2.a.bc

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