# Properties

 Label 189618bf Number of curves $1$ Conductor $189618$ CM no Rank $0$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bf1")

sage: E.isogeny_class()

## Elliptic curves in class 189618bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.v1 189618bf1 $$[1, 0, 1, 176263, -25026532]$$ $$57111104051/58595328$$ $$-621374119036729344$$ $$[]$$ $$3624192$$ $$2.1010$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 189618bf1 has rank $$0$$.

## Complex multiplication

The elliptic curves in class 189618bf do not have complex multiplication.

## Modular form 189618.2.a.bf

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + 3q^{5} - q^{6} + 3q^{7} - q^{8} + q^{9} - 3q^{10} + q^{11} + q^{12} - 3q^{14} + 3q^{15} + q^{16} - q^{17} - q^{18} - 2q^{19} + O(q^{20})$$