# Properties

 Label 221067.x Number of curves $1$ Conductor $221067$ CM no Rank $0$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 221067.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.x1 221067x1 $$[1, -1, 0, -2588031, -1603683284]$$ $$-1484391946907017/1946200179$$ $$-2513455192440566451$$ $$[]$$ $$5760000$$ $$2.4375$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 221067.x1 has rank $$0$$.

## Complex multiplication

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

## Modular form 221067.2.a.x

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 3q^{5} - q^{7} - 3q^{8} - 3q^{10} + 3q^{13} - q^{14} - q^{16} + q^{17} + 6q^{19} + O(q^{20})$$